I've seen recommendations for overhangs to shade windows in the summer
(when the sun is high) and still let the sun under in the winter (when
the sun is low), but I haven't been able to find the equation to strike
the optimum balance. Can you help me find this equation?
Sun Struck in Arlington, TX

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Dear Sun Struck,
Determining the necessary overhang for windows is not totally
straightforward,  so let's just look at the simplest case, which is a
south facing wall/window at solar noon--when the sun is due south.  The
top of the window may be above or below the edge of the roof overhang,
and whether the window in the winter is completely unshaded will not be
considered.  In general, even if we fully shade the window in the
summer, in the winter months the sun will be low enough in the sky that
all or most of the window will receive direct sunlight.

So just consider two dimensions: the distance the bottom of  the window
is below the roof overhang (H) and the distance the roof overhang
extends out from the wall/window (L).  The tangent of (L/H) is the
elevation or altitude angle of the sun at solar noon if the rays just
miss the bottom edge of the window (i.e. the overhang completely shades
the window at that time).

One critical time to completely shade the window is late June when the
sun is highest in the sky.  At that time the sun's declination is 23.5
degrees and its elevation angle = (90 + 23.5 - Latitude) in degrees.
For Fort Worth (about 33 degrees north latitude) this means about 81.5
degrees, for which the tangent is 6.69.  Therefore the overhang must be
about 0.15 of the distance of the window bottom edge below the overhang.

Now June is not really the most critical period in Texas, because our
biggest summer air conditioning demand is in about August.  For mid
August the sun's declination is about 14 degrees. At this time for Fort
Worth the above calculations result in an elevation angle = 90+14-33 =
71 degrees, for which the tangent is 2.9.  Thus the overhang should be
about 0.35 of the vertical distance from the overhang to the bottom edge
of the window.

Of course, one doesn't have to provide the full overhang.  Be sure to
keep in mind that in the summer months when we are most concerned,
preventing direct solar gain at solar noon is the most important.
The Solar Guy