Background:

Vocabulary

• Declination Angle
• Zenith
• Zenith Angle
• Solar Constant
• Solar Insolation
• Hour Angle

Key Concepts

1. The angle at which solar radiation strikes a surface dramatically effects the amount of energy received by the surface.

2. Climate zones, seasonal temperature changes & daily temperature changes are largely controlled by changes in the amount of energy received by the sun due to changes in the angle at which solar radiation strikes the surface.

• Solar Declination angle () the angle between a plane perpendicular to incoming solar radiation and the rotational axis of the earth. The earths’ axis is tilted ~23.5o . The solar declination angle varies from +23.5o on June 21/22 when the earths’ axis is tilted toward the sun, to -23.5o on December 21/22 when the earths’ axis is tilted away from the sun. The solar declination angle is 0o on equinox dates. Changes in the solar declination angle as the earth revolves around the sun creates cyclic changes in solar radiation. These radiation changes contribute to cyclic weather changes that we call seasons. You can get the solar declination angle for any day of the year at the following site. NASA SOLAR DATA

 Dec. 21/22 Jun. 21/22

• The earth is a sphere (360o) that rotates 15o with respect to the sun each hour. During the day rotation causes the sun to rise and set in the sky. Each hour the angle (H) that the solar radiation is striking the surface changes. These changes in solar radiation contribute to cyclic daily changes in weather. The hour angle (H) is the angle that the earth has rotated since solar noon. At solar noon the hour angle = 0o.

• The Zenith Angle (Z) is the angle from the observers zenith point to the suns’ position in the sky. In order to calculate the zenith angle latitude, solar declination angle and hour angle must be considered.

• The solar constant is the average amount of energy striking one square meter (perpendicular to the suns’ rays) each second at the top of the earths’ atmosphere. The satellite measured solar constant is 1366 W/m2. Of this energy reaching the top of the atmosphere as much as 70% can be absorbed & reflected by the atmosphere. Solar insolation is the amount of energy received by the sun at the earths’ surface. On a clear day ~1000 W/m2 reaches a surface perpendicular to the incoming radiation. This energy varies due to the angle of the incoming radiation and again cloud cover.

• Teacher Note: If your students are not comfortable working with trigonometric functions, giving them the zenith angles will allow them to complete the exercise more easily.

For additional background information see Solar Irradiance Brief

Procedure:
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In this investigation students will calculate, graph & compare the solar insolation at different latitudes, dates and times of day. While comparing the calculated insolation values, the student will identify cyclic patterns in seasonal and daily insolation at different latitudes. Show all work on your worksheet

Step 1: Calculate the maximum solar insolation received at your school, that is the insolation at noon on the summer solstice on a clear day.

• First calculate the zenith angle.

• Use your zenith angle to calculate insolation.

I = S cos Z

Step 2: Use the procedure in step 1 to calculate the insolation values for the table on your worksheet. On a sheet of notebook paper show each calculation and box your answer.

Step 3: Use a different color to graph the insolation values for each of the different latitudes.
(Label each line) Answer the graph interpretation questions on your worksheet.
Step 4: You have now calculated solar insolation changes due to changes in zenith angle. You can also examine changes in total daily insolation at equinox & solstice dates by examining seasonal changes in the duration of solar insolation (“length of day”). This will allow students to examine not only the rate of insolation (due to angle) but also the duration of daily solar insolation. Get the sunrise and sunset times for your location on the solstice and equinox dates from the internet linked site below. Times at this site are listed as hours and minutes following midnight. Add the values to the table on your worksheet.
GET YOUR SUNRISE / SUNSET TIMES

Step 5: Use your sunrise and sunset times to calculate duration of sunlight for each of the dates. Add your values to the table.

Step 6: Graph the duration of sunlight for the equinox and solstice dates.
Compare your duration of sunlight graph to your seasonal insolation graph. Describe the relationship between seasonal insolation rate with seasonal insolation duration.

Step 7: Use the procedure in step 1 to calculate the insolation values for your location at the dates and times listed. On a sheet of notebook paper show each calculation and box your answer. In the sunrise and sunset columns fill in the times from your table. Assume that
the insolation value at sunrise and sunset are 0 W / m2.

Step 8: Use a different color to graph the changes in insolation values for each of the different dates. Answer the graph interpretation questions on your worksheet.

Step 9: Now that you have examined solar insolation variations, explain what you have learned by writing your conclusion.

Coding:

Maryland Core Learning Goals (Science): ES
:2:3:1 ES:2:5:1
National Standards (Science): A:3 B:6 D:1
National Standards (Geography): 7:2
National Standards (Mathematics): 9-12 1,1,2,3,4 4:4 9:1

Investigation Discussion and Questions

All investigation calculations and questions appear on the student worksheet. It is suggested that the investigator print a copy of the worksheet and complete it as they go through the activity.

Credits:
Gregg A. Stickler Lee Kyle
NASA Teacher Ambassador NASA Goddard Space Flight Center
GESSEP Program Distributive Active Archive Center
Greenbelt MD