Richard Stovall provides solution for Alternate Exercise #1 from Problem Set #1 of the SolPowerPeople #SolarMOOC

1. Answer to Alternate Exercise
#1 from Problem #1
SolPowerPeople, Inc.
Austin, TX
March 5, 2012

2. Question
 You are designing a ground mount PV array at 30°N
Latitude with multiple rows that faces true south. The tilt
of the modules are 20°. The width of the modules are 39
inches and they will be installed in landscape layout.
What is the closest distance the rows of the modules can
be and not cause any shade during the hours of 8AM and
4PM solar time?

3. 1st Step Determine Height of
back of module
39”
?
20°

4. 1st Step Determine Height of
back of module
We have the
angle theta, and
we have the
39” hypotenuse, and
? we need to know
the opposite, so
we should use
20° the sine
function…

5. 1st Step Determine Height of
back of module
opposite
sin(q )° =
hypotenuse
opposite
sin(20)° =
39"
39” opposite
0.34202 =
? 39"
opposite = 39"´ 0.34202
20° opposite = 13.34"

6. Now solve for shadow length
39”
13.34”
20° ?°
?”

7. Get angle from 30°N SunPath
Chart
Note: question
didn’t specify
time of
year, so we
must assume
shortest day of
the year Dec
21st

8. Get angle from 30°N SunPath
Chart
12°

9. Now solve for shadow length
39”
13.34”
20° 12°
?”

10. Now solve for shadow length
We know the opposite, and we have the angle, and we
want to solve for the adjacent, so we use the tan function
39”
13.34”
20° 12°
?”

11. Now solve for shadow length
13.34"
tan(12)° =
adjacent
13.34"
0.21255 =
adjacent
13.34"
adjacent =
39” 0.21255
13.34” adjacent = 62.76"
20° 12°
?”

12. Now solve for distance
between rows
?” 66.76” (from prev slide)
?°

13. Get azimuth angle from 30°N
SunPath Chart
55°

14. Now solve for distance
between rows
So now we know the angle, and the
hypotenuse, and we need to solve for the
adjacent. We must use cosine function. ?” 66.76” (from prev slide)
55°

15. Now solve for distance
between rows
adjacent
cos(q )° =
hypotenuse
adjacent
cos(55)° =
66.76"
?” 66.76” (from prev slide)
adjacent
0.5735 = 55°
66.76"
adjacent = 66.76"´ 0.5735
adjacent = 38.28"
ANSWER: ~38.28” (depending on how much rounding you did)