Passive Solar Design for New Mexico

Class VI

Air Temp. 49 56 63 70 77 84 91
Mean Radiant Temp. 85 80 75 70 65 60 55

Geographical method: Use SunCharts to make a scale drawing. Overhang is determined by intersection of a summer ray hitting the bottom of the window on the date that you want full shade to begin or end, and a winter sun ray hitting the top on the date you want full sun to begin or end.

Semianalytical method: To get full shade for 3 weeks in summer and full sun for 3 weeks in winter, use a summer ray that is about 2.5 degrees less than at summer solstice and a winter ray that is about 2.5 more than at winter solstice. For 5-6 weeks of effect, use 5 degrees instead of 2.5 degrees. This is the default rule used in the Energy-10 program for overhang sizing. 

Exact Analytical method: First calculate elevations of the sun at noon at solstices or nearby times:

qsun-axis = acos( sin(qtilt)cos(qseason) )  (This yields the angle between the direction of the sun from the center of the earth and earth's axis).

qelevation, noon = asin( sin(qlattitude)cos(qsun-axis) + cos(qlattitude)sin(qsun-axis)  ) (This yields the elevation of the sun above the horizon at noon).

Use: qtilt= 23.47o, qlattitude= 36o, qseason= (days from solstice)/365 x 360o


Time of beginning and end of full shading effect qseason qsun-axis qelevation
Only on summer solstice  0o 66.5o 77.5o
Only on winter solstice 180o 113.5o 30.5o
+/- 3 weeks from summer solstice 20.7o (= 21/365x360o) 68.1o 75.8o
+/- 3 weeks from winter solstice 159.3o (180o - 20.7o) 111.9o 32.1o
+/- 6 weeks from summer solstice 41.4o (= 42/365x360o) 72.6o 71.4o
+/- 6 weeks from winter solstice 138.6o (180o - 41.4o) 107.4o 36.6o

Note that for the 6 week periods, the change in overhang angles is slightly larger than 5 degrees, in agreement with the semi-analytical rule (the Energy-10 rule) described above.

Now calculate overhang ratios:

b = tan(qsummer elevation)/tan(qwinter elevation)

Lheight = Lwindow / (b - 1),  Loverhang = Lheight / tan(qwinter elevation)

Shading period qwinter qsummer b Lheight/Lwindow Loverhang/Lwindow
Only on solstices 30.5 77.5 7.65 .15 .25
+/- 3 weeks from solstices 32.1 75.8 6.29 .19 .30