Name ____________________________________________
Lab 5
Angle of Insolation
Purpose
The purpose of this lab is to have you determine changes in the angle of insolation that occur
throughout the year at different latitudes on the Earth. You will then use this information to
identify the relationship between temperature and angle of insolation, and how this affects the
seasons.
Activities and diagrams in this lab show how Earth-Sun geometry influences seasons and
changes in the amount of daylight we receive. We study the angle of insolation because most
atmospheric processes are ultimately driven by spatial variations in solar energy.
Materials
Calculator (with trigonometric functions)
protractor
Microsoft Excel
Earth-Sun Relationships
The distance between the Earth and the sun averages about 150 million kilometers (93 million
miles). Because of this distance and the Earth’s relatively small size compared with that of the
sun, it is reasonable to assume that the sun’s rays strike the nearly spherical Earth in straight
paths.
The Earth’s axis of rotation is tilted 23 ½°. This tilt is oriented in the same direction throughout
the year, with the North Pole presently pointing toward the North Star, Polaris. The figure
below shows that the Northern Hemisphere is tilted toward the sun during its summer months
and away from the sun during its winter months.
Our seasons occur because of this tilt. As the Earth revolves around the sun, the sun’s direct
rays strike different latitudes. When the Northern Hemisphere is tilted toward the sun, it
receives the more direct and, therefore, more intense rays of the sun. Locations in the Southern
Hemisphere receive less direct solar radiation. Six months later, when the Southern Hemisphere
is tilted toward the sun, it receives the more direct solar radiation.
I hereby declare upon my word of honor that I have neither given nor received any unauthorized aid on
this work.
______________________________________________________
Name ____________________________________________
Lab 5
Procedure A
1. Using a protractor, determine the angle at which incoming solar radiation (insolation) is striking
the Earth’s surface at noon at the three latitude locations shown in diagram A. Record the angle
to the nearest whole degree for each location on Table 5-1.
2. Use the above procedure to determine the angles of insolation for all of the latitude locations
for diagrams B and C. Record the angles for each location on Table 5-1.
3. Using the data on the average monthly temperature for 42°N latitude provided in Table 5-2,
create a line graph in Microsoft Excel that shows the relationship between average temperature
and month during the year. The X-axis should be labeled “Month” and the Y-axis should be
labeled “Temperature (°F).” These headings should be represented as column headings in your
spreadsheet.
TABLE 5-1 INSOLATION DIAGRAM
DIAGRAM A
LATITUDE
ANGLE OF INSOLATION
42°N
EQUATOR
42°S
DIAGRAM B
LATITUDE
ANGLE OF INSOLATION
42°N
EQUATOR
42°S
DIAGRAM C
LATITUDE
42°N
EQUATOR
42°S
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ANGLE OF INSOLATION
Name ____________________________________________
Lab 5
TABLE 5-2 AVERAGE TEMPERATURE TABLE
MONTH
AVERAGE TEMPERATURE AT 42°N (°F)
JANUARY
20.7
FEBRUARY
27.6
MARCH
40.1
APRIL
45.3
MAY
59.3
JUNE
65.8
JULY
67.6
AUGUST
68.5
SEPTEMBER
59.3
OCTOBER
50.0
NOVEMBER
38.0
DECEMBER
22.1
1. Using your data on the angle of insolation for Diagram A, what season of the year do you believe
this diagram represents?
2. Using your data on the angle of insolation for Diagram B, what season of the year do you believe
this diagram represents?
3. Using your data on the angle of insolation for Diagram C, what season of the year do you believe
this diagram represents?
4. What is the lowest angle of insolation that you determined the equator receives throughout the
year, and during what season does it occur?
5. What is the lowest angle of insolation received at 42°N latitude that you determined throughout
the year, and during what season does it occur?
6. What is the highest angle of insolation received at 42°N latitude that you determined
throughout the year, and during what season does it occur?
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Name ____________________________________________
Lab 5
7. Using your data on angle of insolation during spring and fall at different latitudes, what is the
general relationship between angle of insolation and latitude location on the Earth?
8. Using your data, describe the relationship between the season of the year in the Northern
Hemisphere and the angle of insolation.
9. Using your line graph showing the average monthly temperature, describe the relationship
between the angle of insolation and average temperature on the Earth.
Earth-Sun Relationships (continued)



As you have seen in the diagrams, sun angle varies with season and location. Since such
variability greatly influences weather patterns, it is useful to be able to calculate the noon sun
angle for a given latitude. We must first define a few terms:
Solar declination—the latitude at which the sun is directly overhead (90°) at solar noon.
Zenith angle—the angle between a point directly overhead and the sun at solar noon.
Noon sun angle—the angle of the sun above the horizon at solar noon.
o Noon sun angle for a given date and location can be found by using the following:
o 𝑁𝑜𝑜𝑛 𝑠𝑢𝑛 𝑎𝑛𝑔𝑙𝑒 = 90° −
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑠𝑜𝑙𝑎𝑟 𝑑𝑒𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑦𝑜𝑢𝑟 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛
You can approximate the value of the solar declination using the following formula:
𝑆𝑜𝑙𝑎𝑟 𝑑𝑒𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 ≈ 23.5 × sin 𝑁
Where N = the number of days to the closest equinox, expressed in degrees. (By convention, N
is positive between the March and September equinoxes and negative from the September to
March equinoxes.)
For example, on April 20, N=30 (number of days from the closest equinox, March 21) and
𝑆𝑜𝑙𝑎𝑟 𝑑𝑒𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 ≈ 23.5 × sin 30
= 23.5 X (0.5) = 11.75° or 11°45’N
So, on April 20, the sun’s direct rays are at 90° overhead at 11°45’N latitude.
For our location, approximately 39°N, the noon sun angle for April 20 would be:
90°-(27.25°) = 62.75° above the horizon
4
Name ____________________________________________
Lab 5
On December 9, N= (-78). The number of days from September 22 is 78, and it is negative since
it is between the September and March equinoxes.
𝑆𝑜𝑙𝑎𝑟 𝑑𝑒𝑐𝑙𝑖𝑛𝑎𝑡𝑖𝑜𝑛 ≈ 23.5 × sin(−78)
=23.5 X (-0.978) = -22.90° or 22°53’S
So, on December 9, the sun’s direct rays are at 90° overhead at 22°53’S latitude.
For our location, approximately 39°N, the noon sun angle for December 9 would be:
90°-(61.90°) = 28.10° above the horizon
1. Calculate the solar declination on the following dates:
Date
Solar Declination
March 21
June 21
September 22
December 22
Today’s Date
2. Calculate the noon sun angle for New Orleans, USA (30°N), and for Helsinki, Finland (60°N) on
each of the following dates:
Date
New Orleans
Helsinki
March 21
June 21
September 22
December 22
Today’s Date
3. What is the noon sun angle for our location (39°N) today? Show your work.
5
Name ____________________________________________
Lab 5
Daylight Hours
Daylight hours also have an effect on the amount of solar radiation received at a given location.
At any given time only half of the Earth is illuminated (lit up) by the sun. The division between
the light and dark halves of the Earth is called the circle of illumination. This division runs
through the poles during the spring and fall equinoxes. On these dates, every latitude is
bisected (cut in half) and there are 12 hours of daylight and 12 hours of darkness everywhere on
Earth. During most of the year, however, individual lines of latitude will not be bisected but will
be disproportionately divided between light and dark. The figure below illustrates this
phenomenon. You can use the figure to calculate the proportion of each latitude that is
illuminated during the 24-hour day.
6
Name ____________________________________________
Lab 5
4. Use the figure on the previous page and a ruler to estimate what fraction of each latitude is
illuminated during the 24-hour day. From this estimation, record the approximate number of
hours of daylight on each of the following dates:
Date
0°
30°N
60°N
30°S
60°S
June solstice
Equinoxes
December
solstice
5.
Which latitudes experience the greatest seasonal change in daylight hours? Where is the
change the smallest?
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