Most analyses of the pitch and orientation of solar collectors state categorically that the optimal pitch is the latitude and the optimal orientation is due South. However, for both pitch and orientation there is a remarkable amount of tolerance such that 20 degree variations are not too critical. The following graphs are the expected output of a 4KW PV collector installed in Chicago/Evanston, Illinois based upon the PVWatts calculator program available from NREL.

Variations in monthly output as a function of pitch with an orientation of 180 degrees show a large monthly variation that interacts with pitch. The optimal pitch varies by month (and therefore season) and is flatter in the summer and steeper in the winter.

Taking total output across the year, it turns out that 31-33 degrees is about optimal. That is, latitude - 10 degrees. Note that roof pitches between 20-50 degrees produce practically the same amount of energy.
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The optimal orientation of a roof is facing south, but there is a fair amount of play in this so that being off 20 degrees is not too serious.
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Although I can not find heating calculators equivalent to the PV calculators, since both depend upon the same energy source (the sun) the calculations should differ only by a scaling factor (the relative efficiency of PV versus heating). The primary difference is that while a grid connected PV roof should be pitched to maximize annual output, a solar heating system should be pitched to maximize output in the heating season (roughly October - March in Evanston). Taking the monthly data as a function of pitch and summing across the six months of the heating season leads to the optimal pitch about 50-55 degrees.
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Back to the solar energy page. version of March17, 2002
As is true of all web pages, this is part of a constantly growing set of pages. If working off of a printed copy, it is useful to look at the date of the last version. As changes are added to the various pages on, the "What's New" page will track changes.
Prepared by William Revelle. Comments to W. Revelle