CE 335
Programming Assignment 2
Optimization: Orienting solar collectors
The orientation of photovoltaic panels and solar water heaters relative to the sun determines how much
sunlight they absorb, which we generally want to maximize. The sun's direction changes over the
course of the day and through the seasons, forcing tradeoffs if we have a fixed collector that will not
be moved to track the sun; in some cases the collector can turn to follow the sun, like leaves do.
The sun's location in the sky at different times of day and year is given by the following equations:
Eq. 1:
γ
= 2 *
π
fractional_year
Eq. 2:
h
= 2 *
π
(fractional_day  0.5)
Eq. 3:
D = 0.006918  0.399912cos( ) + 0.070257sin( )  0.006758cos(2 ) + 0.000907sin(2 ) 
γ
γ
γ
γ
0.002697cos(3 ) + 0.00148sin(3 )
γ
γ
Eq. 4:
cos( ) = sin(
φ
lat
)sin(D) + cos(
lat
)cos(D)cos(
h
)
Eq. 5:
tan( 
) = sin(
θ π
h
) / (sin(
lat
)cos(
h
)  cos(
lat
)tan(D))
where the various symbols are:
fractional_year
the time of year,
going from 0 at the beginning
of the calendar year to 1 at the end of the year
γ
the time of year expressed as an angle
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 Spring '11
 Lybas
 Tan, γ, 24 hours, 1350 W, 0.71 radian

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