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program_2 - CE 335 Programming Assignment 2 Optimization...

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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 trade-offs 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 fractional_day the time of day,

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