Sunday, May 3, 2020

Design - Solar Collector - Maximizing Solar Gain

The previous post on the solar collector for the AGS system dealt with the mechanisms for trapping solar energy and converting it to usable heat.  This post discusses the factors that go into maximizing the amount of solar energy collected.

Original Assumptions
My early thinking, that appears in at least one prior post, was that the best tilt for the glass and steel would be perpendicular to the sun angle for St Louis shortly after the summer solstice (June 21), say July 21.  Since the choice was empirical, I wanted to flesh it out with data if possible; hence, the following analysis based upon three factors -- optimal sun angle, warm weather collection period and available daylight.

Optimal Sun Angle
NOAA Solar Position Calculator is seemingly a useful tool for knowing the elevation of the sun angle from horizontal. However, Gary, my mathematician brother-in-law, calculated the angles and found the NOAA data to be incorrect. Following are his sun angle calculations (rounded up or down) for St Louis.  The optimal tilt for the glass and galvanized steel roofing in the collector would be 90 degrees from the sun angle during the warm season but the question is what date would be best to use as the default.  For the sake of discussion, the  figures for five scenarios are listed below :  

     June 21:    Sun elevation from horizontal = 75 degrees; collector glass angle = 15                       degrees from horizontal

     July 21:  Sun elevation = 72 degrees; glass angle = 18 degrees

     August 21:  Sun elevation = 64 degrees; glass angle = 26 degrees

     September 21:   Sun elevation = 52 degrees; glass angle =  38 degrees

     January 21:  Sun elevation = 32 degrees; glass angle = 58 degrees

A default date of July 21 with a sun angle of 72 degrees is only 3 degrees less than June 21 and, by observing the play of the sun in the collector shell for a few summers now, I think that the difference between the two is moot, i.e., the additional amount of sun entering the collector on June 21 vs. July 21 is negligible.  

The sun angle for January 21 was included above to contrast the difference between the typical passive solar design that uses the energy from the low-angle winter sun versus the high-angle summer sun that energizes our AGS system.  For solar gain in winter, the optimal tilt for our 38 degree St Louis latitude of, say, greenhouse windows, would be tilted 58 degrees off horizontal to be at 90 degrees to the sun angle compared to the 18 degrees off horizontal that optimizes the output of our solar collector on July 21 -- a difference of 40 degrees.

Parenthetically, the south facing windows of our house are 90 degrees from horizontal rather than the 58 degrees that is optimal for January 21. The 32 degree difference might be important for a classic winter-centric passive solar build but, as detailed in a prior post, maximizing solar gain in winter is not very important for our Annualized GeoSolar System, especially after the first couple of years.

Warm Weather Collection Period
In order to keep cold air out of the AGS system, the north ends of the conduits will be capped during the cold months -- roughly from the end of September until the beginning of April.  Consequently, the question becomes, "Shouldn't the default date for the sun angle fall in the middle of the six-month April through September collection period?"  If so, it would be sometime in June.  However, it is more likely that lingering cold weather in the spring will delay opening the conduits than early cold weather will cause them to be capped prematurely in the fall, thereby skewing the midpoint of the collection period backward to, say, sometime in July.  So, again, any advantage of a June default date over a July date is questionable, particularly in view of the amount of cloudy weather in the spring as discussed below and recurring warmer autumns due to global warming.

Available Daylight
In addition to optimal sun angle and which months are included in the collection period, it is useful to consider the available daylight during the collection period. NOAA's Sunrise-Sunset Calculator is helpful in this regard.  Here are some representative values spanning the seven months that would be in play as the optimal collection period.

     April 1:  12 hours, 40 minutes

     May 15:  14 hours, 18 minutes

     June 15:  14 hours, 51 minutes

     July 15:  14 hours, 35 minutes

     August 15:  13 hours, 39 minutes

     September 30:  11 hours, 48 minutes

     October 30:  10 hours, 36 minutes

These data seem to indicate that a June 21 date in the middle of a six-month collection period -- April through September -- would provide more available daylight than would a mid-July date with a six-month collection period -- May through October.  
However, according to Climate for St Louis, there is much more rain in April through June than in August through October.  More rain means less available sunlight.  Less available sunlight in spring and early summer therefore makes May through October a more attractive collection period than an April through September period despite the latter's shorter days and makes July 21 a better midpoint than June 21.

Three factors influence the choice for the best date on which to base the angle for the glass and steel panels:  (a) sun angle from horizontal, (b) the timing of the collection period and (c) the available daylight during the collection period.  A close look at sun angles and collection periods results in essentially a wash between June 21 and July 21. But the third factor, the available daylight/sunlight during the collection period, seems to tip the scales in favor of July 21 which validates my original hunch.