Winter-Solstice Shadow Ratio & Azimuth Table
Determine objects’ shadow lengths and direction on the day with the longest shadows of the year (the winter solstice) using the following table of shadow ratios and sun’s azimuth angles for your latitude…
Use the ratio 1 : x to get the length of the shadow cast by an object (tree, cistern, house) for each foot (or meter) of height. Multiply the height of the object (in feet or meters) by x to get the length of the shadow (in the same units of measurement).
To get the direction of the shadow cast by an object, look at the Azimuth angle—the angle of the sun’s location east or west of True South in the northern hemisphere or of True North in the southern hemisphere. Note that when the position of the sun is to the east, it will cast a shadow to the west of any object. (See figures below the table for examples, and the “Integrated Design Pattern Five: Maintaining Winter Sun Exposure” section of Rainwater Harvesting for Drylands and Beyond, Volume 1, 3rd Edition, for still more examples, explanation, information, and tools.)
For more examples, explanation, and information on how to use the this table and other passive solar design tools, see Integrated Design Pattern Five: Maintaining Winter Sun Exposure section of Rainwater Harvesting for Drylands and Beyond, Volume 1, 3rd Edition, by Brad Lancaster.
Azimuth angle of the sun at 3 P.M. on the winter solstice at 32º N latitude. The Azimuth is the sun\’s location in degrees east or west of True South in the northern hemisphere, or of True North in the southern hemisphere. Using winter solstice 3 P.M. shadow ratio of 1 : 2.77 from table to determine length of shadow cast at 32º N latitude, and using Azimuth angle of sun’s location from True South to determine direction of shadow Shadows cast at 3 P.M. on winter solstice at 32º N latitude once tree reaches mature size
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