The latitude at which the noon sun is directly overhead is defined as the sun's declination. For example, if the sun appears directly overhead at 20°N latitude, the sun's declination is thus 20°N. Figure 7-3, known as analemma, shows the declination of the sun throughout the year. Thus, if you would like to know where the sun will be directly overhead on September 20, you can look on the analemma and find that it will be at 1°N. Given the declination, the noon sun angle at a particular latitude on any given day can be calculated.
Figure 7-3. The analemma, a graph illustrating the latitude of the overhead noon sun throughout the year.
Figure 7-4 shows that for each degree of latitude that the place is away from the latitude where the noon sun is overhead (declination), the angle of noon sun becomes one degree lower from being vertical (or 90°) above the horizon. Noon sun angle for any given latitude on any given day can be calculated using the following equation:
Noon Sun Angle = 90° - (Latitude +/- Declination)
In this equation, use " - " when the latitude and declination are on the same hemisphere and use " + " when they are on the opposite hemispheres. For example, on April 11, the declination is 8°N, the noon sun angle at Springfield, Illinois (40N) on April 11, therefore, should be 58° (90° - (40°N - 8°N).
Figure 7-4. Noon sun angle calculation. The example in this figure illustrates how to calculate the noon sun angle for a city 40° north of the equator (like Springfield, Illinois) on December 22.
Questions
Based on Figure 7-3, the sun shifts its position between which two important latitudes (find the terminologies for these two latitudes in Fig. 7-4). (2 points)
Using the analemma (Fig. 7-3), determine the declinations on each of the following dates. (6 points)
August 10
September 21
June 21
October 15
December 22
March 21
Calculate the noon sun angle in Grayslake, Illinois on each of the dates listed below. (6 points)
Noon Sun Angle in Grayslake on
August 10
September 21
June 21
October 15
December 22
March 21
Obtain the average temperature in Grayslake on each of the dates listed below using a weather station online. (6 points)
Average Temperature in Grayslake on:
August 10
September 21
June 21
October 15
December 22
March 21
Plot the noon sun angle and temperature on each of the dates you obtained in Questions 3-4 on the graph provided below and connect your temperature and noon sun angle plots using smooth lines. Discuss the relationship between noon sun angles and average temperature in Grayslake throughout the year based on your graph. Use the right vertical axis to show temperature variation from -30° F at bottom and +105° F on top (label temperature value at equal amount interval in between: 2 units for every 5°F). Use the left vertical axis to show noon sun angle, with 0° at the bottom and 90°F on top (label noon sun angle value at equal amount intervals in between: every 3 units per 10°). (4 points)
J F M A M J J A S O N D
Months
Figure 7-5. Variation of temperature and noon sun angle in Grayslake.
brief paragraph summarizing the yearly movement of the overhead noon sun and how the intensity of insolation aries in Grayslake throughout the year. (2 points)
Calculate the maximum, minimum, and average noon sun angles at the place in Grayslake. Show your calculations. (3 points)
Maximum noon sun angle:
Minimum noon sun angle:
Average noon sun angle:
When the noon sun is directly overhead a ship in the Pacific Ocean on October 16, the ship's latitude is . Explain your answer. (2 points)
