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```					Why Is Alaska So Cool?                                   Sunlight Intensity Accumulator

Activity 8: Investigation in Sunlight Intensity
Part 1: Collecting Data
Guiding Question
Why is Alaska so cool (with all that daylight)?

Prediction of results
Why do you think Alaska is so cool?

Objectives
After completing this investigation, a student will be able to describe a procedure
by which sunlight intensity may be measured, recorded, and modeled
mathematically; and will infer a provisional answer to the guiding question.

Materials
TI-83 Plus, CBL, light sensor, 1 m wooden dowel or other stick, electrical or
plastic tape, daily log, program CBL/CBR already in the calculator.

Introduction
In this investigation, students from various locations will collect solar intensity data by
means of a TI-83 Plus calculator and CBL unit. The data will be collected at noon on the
equinox (or as near to that date as possible considering weather) from various stations,
and will be correlated with latitude and weather conditions. The reason for collecting
data on the equinox is that this mitigates duration variation.

Variable conditions we anticipate affecting solar intensity include the following:
weather (degrees of cloudiness and of haze), latitude, relative distance from the sun (to
a minor degree), and distance of light travel through earth’s atmosphere.

As we apply computational science to the collected data, we expect to discover a
mathematical model that reasonably accounts for the data, and that will adequately
predict intensity for other latitudes.

General Plan
1. A week before the equinox: Complete a trial run of the investigation following
the instructions exactly, in order to know what to expect from your equipment
and to eliminate problems for the day of the actual investigation. You will use
the CBL to collect sunlight intensity samples automatically for two hours, from
one hour before through one hour after solar noon. Use the determination of
solar noon that you found from the Solar Angle investigation. You will also

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record data for the solar angle and observation of sky conditions during the time
you are sampling the sunlight data.
a. Record your activities in your daily log, and also indicate any difficulties
you had in following the procedure.
b. Record the data in a table as described on page 110.
2.    On the first sunny day after within a week of the equinox, compete the following.
a. Two hours before solar noon – Gather the instruments you will be using,
and set up your equipment so that you are ready to conduct sunlight
intensity data collection for a two hour period.
b. One hour before solar noon – begin collecting sunlight intensity data
following the instructions below beginning with the section title Rate of
Sampling. Continue collecting the data through solar noon until one hour
after solar noon.
c. Measure the solar angle at the beginning of your data collection, at the
midpoint of the data collection, and at the end of the data collection.
d. Observe and record the sky conditions at the beginning of your data
collection and every 15 minutes during the data collection, or as necessary
as the conditions change.
e. One hour after solar noon – stop collecting solar intensity data,
disassemble and pack equipment.
f. In your daily log, summarize what you have done today.
g. Record the data in a table as described on page 110.
3.    On the day of the equinox (or first clear day after it):
a. Repeat steps a-g above.
b. Determine which set of data best represents the sunlight intensity on a
clear day and use that data.
4.    Keep a daily log for the course of the data collection. Include the date, the
chronological time you began the collection, the times when you re-aimed the
light sensor, and sky conditions (clear, hazy, cloud passing by, and so on).
5.    After data from all stations has been collected, your teachers will distribute the
information. You will then analyze the collected and compiled data, performing
a regression analysis on it, answering questions, and reaching appropriate
conclusions.

Rate of Sampling
When you collect samples of data at different times or places of the same phenomenon,
this is called “sampling.” You will be taking samples of sunlight intensity over a period
of time, every so often. In the course of setting up the calculator’s sampling program,
you will need to indicate the number of samples you will take and the time interval in
seconds between data samples.

In order to help make sure that the data are not spurious or inappropriate, you will take
a number of samples, one sample every five (5) minutes over a two (2) hour span. How

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many samples will you take, and what is the time interval in seconds between samples,
then? The following equations solve the questions:

Number of samples = 2 hr x 60 min/hr / 5 min = 120 min / 5 min = 24;
Time interval in seconds = 5 min x 60 s/min = 300 s.

So, you will take 24 samples with a time interval of 300 seconds between samplings.
When the sampling is completed, you will record your data and find the average of the
values of your samples for the light intensity at solar noon.

Equipment Setup
Please gather the equipment indicated in the materials section on the first page of this
lesson plan.

Aiming the Light Sensor to the Sun

1. This investigation needs to take place in direct sunlight, without any shadows
whatever throughout the duration of the data collection (if at all possible).
Conduct the data collection in a place where you will have unobstructed view of
the sun for the two hour time interval. Do not conduct it through window glass,
though you might be able to use an open, unscreened window. The better
location is outside in an open area. If you live in a place where the sun does not
shine directly, go to a nearby place such as a park or field.
2. Throughout the sampling time for sunlight intensity, you will need to have the
light sensor aimed as directly toward the sun as you can. The sun will appear to
be moving through the sky (through a small arc, however) over the two hours, so
you will need to make periodic adjustments to the light sensor’s orientation
toward the sun. CAUTION: Do not look directly at the sun! One way to help
make sure the light sensor is at the best aim is to have the light sensor create the
smallest shadow possible at a given height
from the ground.
3. To accomplish this, you may use a wooden
dowel or suitable stick; a wiener roast type
of stick would be fine as long as it is rigid
enough not to bend. See Figure 1. If the
ground is soft enough, press the dowel
into the ground. Otherwise support it so
that it will stay in an upright position. Aim
the light sensor toward the sun, and tape it
to the dowel in that position. You can fine
tune the aim by pivoting the sensor up or
Figure 1 – Light Sensor in Place              down as necessary and by turning the
dowel right or left. The smaller the

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shadow, the more directly it is aimed to the sun.
4.    Once the data collection has begun, please do not change the height of the sensor
on the dowel. You may turn the dowel or pivot the light sensor, however.
5.    During the sampling process, check to see that the light sensor is aimed
appropriately every fifteen (15) minutes.
6.    You do not need to hold the CBL unit and calculator in your hands the whole
time, but please do not place them directly on the ground. Moisture is not a
friend to electronic equipment. You may place your equipment on a plastic sheet
on the ground or a table if one is handy.
7.    Do not leave your equipment unattended. Stay with your equipment until you
have completed data collection and have placed your equipment in its storage
area.

As you have connected the calculator and CBL in other investigations, please do so
again. You will run the APPS program called CBL/CBR in order to collect sunlight
intensity data. (This application is described in the TI-83 Plus Manual on pages 14-16
through 14-26.)

1. Turn on the calculator, and press CLEAR twice, then press the blue APPS
key. You have usually used the PRGM key to find programs, but this is a
different type of program. It works as other ones you have used. Your screen
should look like the following:

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2. Choose 2:CBL/CBR, and the next screen is:

3. Follow the instructions, and the next screen is:

4. Since we are planning to log data over a period of time, choose 2:DATA
LOGGER, and the next screen shows (your screen may have different values):

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5. You have several parameters to set on this screen.
a. Press the     cursor key to choose Light and press ENTER .
b. Press       cursor key to #SAMPLES:, and type 24, press ENTER . The
cursor drops automatically to the next line.
c. At the INTRVL(SEC) line, type 300. Press ENTER . The cursor
automatically drops two lines.
d. At the PLOT line, choose RealTime and press ENTER        .
e. On the DIRECTNS: line, choose ON, and ENTER           .
The cursor drops to GO…, and the resulting screen must look like the
following:

If your screen has other values or other selections than the screen above, then
move the cursor (up or down), select and enter the parameters (selections and
numbers) as described in Item 5 a-e, above.
6. When all the values and choices are correct, press ENTER . Follow the
connection instructions as you have in other investigations.
7. When the connections between the probe, CBL, and calculator are complete and
you have received the STATUS: O.K. message, press ENTER . The next screen
is:

8. You are now ready to begin collecting light intensity samples.

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Why Is Alaska So Cool?                                   Sunlight Intensity Accumulator

Sampling Light Intensity

1. When the time is right (one hour before solar noon on the summer solstice), do as
the message summons you to do: Press ENTER . The screen changes to show a
coordinate plane, and nothing else seems to be happening. But in fact, the
program is running and you are collecting sunlight intensity samples, one every
300 seconds for the next two hours.
2. In your daily log, note the actual date and chronological time you pressed the
Enter key to start sampling.
3. Note that the CBL unit will show values in its screen that will be updated every
five minutes, and it will flash the word SAMPLING for the entire time. You may
also see a short moving line in the upper right hand of the calculator screen, to
indicate that it is working. Periodically, a dot appears on the coordinate plane
corresponding to the sampled light intensity. You will have 24 of these dots in
place by the end of the sampling period. They will appear in a graph on the
screen. (The program sets up Plot 1 to plot these points as they are collected.)
4. What if the CBL or the calculator is not doing what the last paragraph said? If
things are not working properly, turn everything OFF, and start over with
“Readying the CBL and Calculator” in Item 1 above. Be sure to note in your daily
log that you had to start over, and log the time when you actually began the
sampling properly.
5. When your data collection is completed, please turn off the CBL and disconnect
it from the calculator. Place the CBL, light sensor, and link cable in the protective
case. You will not need to use the CBL unit or light sensor. Indeed, you have now
completed all the activities in which these are used. If the calculator still shows
the moving dots in the upper right corner of the screen, press  to stop the
program from running.
6. Did your collection go well? If so, congratulations – good job!

Recording and Sending Collected Data
When the program collected the sunlight intensity, it stored the data in two lists named
LIGHT and TLGHT (for “light intensity” and “time interval,” respectively). You cannot
see these lists directly, but you can copy them to L1 and L2 lists, and then you can see
them.

The following procedure will step you through the process so that you can read the
lists. These instructions will not explain why you are doing the procedure, only that
these are the steps to take. If steps are not self-evident, and you are curious about them,
you may read the TI-83 Plus Manual, page 12-11, for an explanation of Entering a List
Name in the Stat List Editor.

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1. Turn on the calculator and press STAT ENTER . You are in the list editor
screen and it will look something like the following, but may have different
values in the lists:

2. Press     to move the cursor up to highlight the list name L1. Press 2nd    STAT
to access the LIST NAMES menu and the screen shows:

3. Scroll the cursor down to 7 LIGHT and press ENTER . The screen shows L1 =
LLIGHT at the bottom of the screen (it may have different numerical values):

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4. Press ENTER ; the L1 list receives the values for your sunlight intensity (they are
probably different from the values below):

5. Press        to move the cursor to the name for L2. Press 2nd STAT .
6. Scroll down with     until TLGHT scrolls into view and is selected.
7. Press ENTER , and the screen returns similar to the following with L1 = LTLGHT
at the bottom (but with different values):

8. Press ENTER , and the L2 list receives the values for the time intervals. L2
values should be the same as the screen above (0 through 6900), though L1
values will not be.
9. Using the cursor keys, you may now scroll up and down, and see all the data
readings you took of sunlight intensity (L1) and the time interval (L2). You
should have 24 data items in each list.

Once you have copied the data into the lists, you will need to transcribe the data you
have collected into Excel, into a word processing document, or onto a sheet of paper if
necessary. Complete a chart like the one below to record the time intervals, the actual
time you started the recording, the three solar angle measures, and the observation of
sky conditions.

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Sunlight Intensity Accumulator                                  Why Is Alaska So Cool?

At the top of the chart, record this information:
Data collected on __________ (date)
Data collected at _________________ (location) at _________latitude and
________ longitude.

Time of day       Solar Intensity    Time interval      Solar Angle       Sky conditions
(L1)               (L2)               measure
11:00 AM               .92515               0           53.6             Partly Cloudy
.91291              300
.                  .
.                  .
.                  .
12:00 N                .88398              3300         54               Hazy
.                  .
.                  .
.                  .
1:00 PM                .87285              6900         53.5             Cloudy

Determine the average value of the sunlight intensity for all the samples. Include this
average at the bottom row of your table.

A way to determine the average, or mean, of the L1 list is to have the calculator do it for
you. Go to the home screen, then press 2nd STAT                 to move to the MATH
menu. Press           ENTER to select 3:mean(. Now press 2nd [L1] ENTER , and
this returns the mean for the list.

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Concluding Questions (Part 1)
1. Record the date, location and chronological time of your data collection.
(If you’ve not already done so, record this information in your daily log as well).
2. To what degree did your preparation over the past couple of days help in being
3. What difficulties did you encounter in collecting sunlight data? Please discuss:
a. Equipment set up
b. Collection of data (sky conditions, aborted starts, etc.)
c. Transcribing and sending data
4. Reflect: What type of regression analysis do you anticipate will be appropriate
for the data collected? Why?

Hand in to your teacher the data in the Excel spreadsheet or word processing
document. (If you do not have a word processor, write the information on a sheet of
paper neatly.)

Part 2 of this investigation, creating a model by conducting a mathematical regression
analysis on all the data collected from students in various stations, will take place after
that data has been collected and compiled.

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Activity 8: Investigation in Sunlight Intensity
Part 2: Analysis of Accumulated Data

A provisional answer to a question indicates that when more knowledge becomes
available, the answer to the question may change. Students will be able to use the
collected data to create provisional models and to provide provisional answers to the
guiding question.

This part of the investigation will involve analyzing data collected from the various
stations. You will have data that includes the sunlight intensity at solar noon, the solar
angle at the location of the intensity readings, the latitude and longitude of the point of
data collection, and the distance from the sun. The distance from the sun varies for
different latitudes on earth as shown in the diagram below:

90 N
x               d
Night                            A
r
c
23.5 N        Sun’s rays
        r
0
(equator)
Day
23.5 S

90 S
The distance from a point on earth to the sun can be represented by d + x where d is the
average distance to the sun at the point where the sun shines at a 90 angle and x is the
additional distance to the particular point on earth. This distance can be calculated
using trigonometric relationships and is described in the document Mathematical
Calculation of Distance from the Sun. The distance is calculated for you on the Excel

When you are instructed in the questions below, please enter the data into the TI-83
Plus and into Excel and create mathematical models by performing a regression
analysis on the data.

1. Create a model of intensity versus latitude.
2. Create a model of intensity versus longitude.
3. Create a model of intensity versus solar angle.

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Sunlight Intensity Accumulator                                Why Is Alaska So Cool?

4. Create a model of intensity versus distance. Be sure to include an appropriate
distance scale 0 km to approximately 155,000,000 km. (To change the scale on an axis
in Excel, right click on the scale on the axis you wish to change, then select Format
Axis. Click on the Scale tab and enter the minimum and maximum values you wish
to show on the scale. Be sure to uncheck the box in front marked “auto” which sets
the scale automatically.)

5. Think through this: Is it reasonable for you to assume that you have collected
enough information from this investigation to answer definitively the overall
guiding question? Why do you say so?

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

6. What type of regression or model have you decided best represents the sunlight
intensity data? Why do you say so?

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

7. Offer a provisional answer to the project question: “Why is Alaska So Cool (when
the days are so long)?”

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

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Why Is Alaska So Cool?                           Sunlight Intensity Accumulator

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

Activity 8                                                              Page 15

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