# Hands On Physics

### Haze Concepts SUN ANGLEDetermining the Sun's Angle

You will need to know the angle of the sun above the horizon to compute the air mass. You can determine this angle using the shadow method, a digital level, a spreadsheet formula or by using various software programs. The TERC VHS-1 spreadsheet can assist you in your calculations, and can be downloaded from: ftp://concord.org/pub/haze/vhs1-download/If you measure the angle of the Sun directly, be sure to do so immediately after making the observations. In any case, it's very important to record the date and the exact time of your observations. The time information will permit you or others calculate the Sun's angle using a computer spreadsheet at a later date should you or they elect to do so.

You can measure the angle of the Sun to within about 1 degree or so by using the TERC VHS-1 as a simple sun dial. You'll need a bubble level vial (also known as a spirit level) like those used in a carpenter's level.

Figure P1

The bubble vial should rest along the corner formed by the side of the case and the angle bracket. Cement the bubble level to the side of the VHS case adjacent to the Sun Target angle bracket.
Cut a strip from a self-adhesive label measuring 8 cm long and about 1 cm or so wide. Make a ruler by carefully placing lines across the strip at 1 mm intervals. Number each tenth line (1, 2, 3, etc.).
Attach the self-adhesive ruler you have made to the side of the VHS case between the two angle brackets as shown in Fig. P1. The first line on the ruler should fall in line with the front surface of the Sun Target.
To measure the Sun's angle over the horizon, place the TERC VHS-1 on its side with the toggle switch pointed toward the sun. Tilt the instrument until the bubble is centered.
Notice how the Sun Target casts a shadow along the ruler. When the bubble is centered, measure the length of the shadow cast by the Sun Target.
Record the length of the shadow, the date and the exact time of your measurement in your notebook.
The tangent of the sun's angle above the horizon is the length of the upper vane divided by the length of the vane's shadow. Use a calculator to find the tangent of the angle.
When the tangent is displayed in the calculator's readout, press the cotangent (TAN^-1) key to find the Sun's angle in degrees above the horizon. Enter the angle in the notebook.

### Inclinometer or Digital Level Method

An inclinometer is a protractor with a weighted needle or dial. When the base of the inclinometer is level, its indicating needle or dial points straight up (90 degrees). When the inclinometer is tilted, the needle or dial remains stable, thus indicating the degrees of tilt. SmartLevel and other digital carpenter's levels can also be used to find the Sun's angle.

Since there are many different kinds of inclinometers and digital levels, we can't provide detailed instructions on how to use each of them. One method is to attach a straight hollow rod along the base of the level. A small piece of paper should be mounted near and in line with the end of the rod away from the Sun. The base of the inclinometer or level is tilted toward the Sun until a beam of sunlight emerges from the end of the rod and forms a bright circle on the paper. The instrument is pointed directly at the Sun, and the angle on the dial or readout indicates the Sun's angle above the horizon.

Digital levels work best and are more accurate, but they are more expensive. Since the pointer or dial of a mechanical inclinometer sometimes sticks, it might be necessary to tap the instrument when it is at the desired angle.

### Computer Programs

The TERC VHS-1 spreadsheet provides the Sun's angle and the air mass for any location on any day and time. Various computer programs are available that give the angle of the sun for any time on any day of the year for any location on Earth. Examples of such programs include AstroCalcTM and AstroCalc PlusTM (Zephyr Services, 1900 Murray Avenue, Pittsburgh, Pennsylvania 15217 USA). SunTimes, also available from Zephyr Services, gives the angle of the Sun at solar noon and at 30-minute intervals for any day and any location you specify.

#### Finding Local Time

Solar noon for your location is not necessarily when your watch shows 12:00, especially if daylight savings time is in effect. Complete details about how to determine the local time for your location are given in various books and magazines about astronomy and sundial making.

Briefly, the Earth rotates 360 degrees in 24 hours. This is equivalent to 1 degree in 4 minutes or 15 degrees in one hour. The standard time longitudes or meridians range from 45 to 165 degrees west in increments of 15 degrees. Therefore, the time at each meridian is one hour earlier than the previous meridian.

To find your local time, first find the distance in degrees between your longitude and your time meridian. Multiply the number of degrees by four to obtain the correction for your location. If you are east of the time meridian, add the correction to the standard time for your area; if you are west of the meridian, subtract the correction from the standard time. The result is known as your local mean time.

For example, the longitude for Omaha, Nebraska, is 96 degrees, 6 degrees west of the standard time meridian of 90 degrees. This means the time correction is 6 x 4 or 24 minutes. Since Omaha is west of the meridian, 24 minutes must be subtracted from Central Standard Time to arrive at the local mean time for Omaha.

Over the course of a year, the Earth's orbit causes the sun to run either ahead of or behind local mean time by as much as 16 minutes. The actual difference between local mean time and the actual or apparent time is called the equation of time. Computer programs that compute the sun's angle, such as the TERC VHS-1 spreadsheet, automatically determine and correct for the equation of time. For additional information, see Further Reading.

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