Sun Angles and Seasons in Africa
Background: The angle of the sun above the horizon is important.
 When it is high in the sky, the sun adds a lot of energy to each square foot of
ground. (You can get a sunburn very quickly!)
 When it is down near the horizon, its energy is spread out over a larger area, and
each square foot of surface gets less.
Data. This table shows the sun angle on different days in Chicago and nine cities in Africa.
The sky is not always clear, however, and therefore people could not measure the sun angle
on every day. Your task is to use logic and math to figure the sun angle for the cloudy days.
Noon sun position, in degrees down from overhead
Urban Area
Country
Latitude
Population
(millions)
Mar 21
Chicago
U.S.
42°N
8.0
42 to S
Cairo
Egypt
30°N
6.7
30 to S
Timbuktu
Mali
17°N
0.1
17 to S
Khartoum
Sudan
15°N
5.3
15 to S
Lagos
Nigeria
7°N
8.4
7 to S
Kampala
Uganda
0°N
1.7
4 to N
Nairobi
Kenya
2°S
3.4
6 to N
29 to N
Luanda
Angola
9°S
5.2
9 to N
13 to N
32 to N
Johannesburg
S Africa
26°S
26 to N
30 to N
49 to N
Capetown
S Africa
34°S
34 to N
cloudy
57 to N
8.2
3.6
April 21
June 21
Sept 21
Oct 21
19 to S
26 to S
7 to S
13 to S
Dec 21
65 to S
30 to S
44 to S
53 to S
17 to S
31 to S
40 to S
15 to S
29 to S
38 to S
21 to S
30 to S
26 to N
12 to N
3 to N
34 to N
20 to N
11 to N
16 to N
9 to N
Procedure:
The first two are easy On March 21, the sun is directly overhead at the Equator.
 Write “straight up” in the blank for Kampala on March 21.
 In all other places, the noon sun is down from directly overhead. On March 21, that
downward angle is equal to the latitude of the place. For example, Cairo‛s latitude is
30 degrees north, and therefore people in Cairo see the noon sun exactly 30
degrees south of directly overhead on March 21.
Follow the directions on the next page to fill in the other blanks.
Sun Angles and Seasons in Africa
1 Figure the sun angle for Nairobi on March 21, and write the number in the proper blank.
On June 21, the noon sun shines directly down on the Tropic of Cancer, about 23 degrees of
latitude north of the Equator. People in Kampala, therefore, see the noon sun 23 degrees north
of directly overhead on June 21. At Khartoum, it is 8 degrees north of overhead.
2 Figure the sun angle for Timbuktu on June 21, and write the number in the proper blank.
On April Fool‛s Day (April 1), people in Kampala see the noon sun 4 degrees down to the north.
The sun is therefore straight up for people who live at a latitude of 4 degrees north.
In Lagos, at 7 degrees north latitude, the noon sun would be 3 degrees south of overhead.
3 Figure the sun angles for Chicago and Khartoum on April 1, and write them in the proper
blanks.
Use your analytical skills to figure the sun angles for the other blanks on the table.
4 Then, write a short paragraph to compare sun angles at Chicago and these African cities.
Your paragraph should include a brief but clear description of the angles in each season, as well
as the likely consequences for temperatures at these places.
Teacher’s Guide:
Sun Angles and Seasons in Africa
Overview: Students examine a table of sun angles at different
latitudes and seasons; they fill in a number of blank lines,
depending on how much practice they need to get the main points.
In doing this activity, they should acquire an intuitive grasp of the
way that sun angles drive the entire climate “machine” of the earth.
Grade: 7 - 12
Related Discipline: Earth science
CC Standard: math, writing
Time: ½ to 1 class period
Climate patterns underlie virtually every other environmental pattern on earth – the locations of
thunderstorms, fires, soil-forming processes, plants, animals, and human food production. There are
many ways to learn about climate, but it is worth noting that one of the ways that might seem harder at
first – understanding the pattern of sun angle – may actually be one of the most efficient ways.
Procedure: This activity can be run as individual, group, or whole-class inquiry. The worksheet is
more or less self-explanatory – make sure students know realize they can use the answers already
provided as a way to check their reasoning before they try the blank lines.
Answers: On March 21, the sun is directly over the equator, and therefore the answer for any other
latitude is the latitude. Kampala is 0 degrees (directly overhead) and people Nairobi would see the
noon sun only 2 degrees down, in the north because Nairobi is south of the equator.
On April 1, the sun shines directly down at 4 degrees north. Chicago therefore sees the noon sun 4
degrees less than its latitude, or 38 degrees down toward the south. The down angles at Khartoum and
Lagos are 11 and 3 degrees.
On June 21, Kampala sees the noon sun 23 degrees down to the north; Khartoum 8N, Timbuktu 6N.
September 21 is like March, so the angles at the four cities are equal to their latitudes: 42S, 7S, 0, 2N.
On October 31, the angles are 14 degrees south of the latitudes: 56S, 14S, 12S, 5S
And on December 21, the angles are 23 degrees south of their latitudes: 23S, 25S, and 34S
Chicago never sees the sun directly overhead – it is always down to the south, 19 degrees down in
summer, 42 in spring and fall, and 65 in winter. Most of the African cities see the noon sun directly
overhead on at least one or two days every year. Places near the equator see it n orth of overhead in
summer and south in winter.
Debrief: Perhaps mention that it requires some Common-Core like mathematical reasoning to solve
this problem, so we are in effect “double-dipping” and meeting two objectives with the same
worksheet.
Vocabulary: sun angle degree latitude season zenith horizon intensity (perhaps even cosine
relationship, if that kind of math extension is desired)
Extension: Convert from zenith angles (degrees down from directly overhead) to horizon angles
(degrees up from the horizon)
Setup: