Calculating the angle of shade created by the sun can be very helpful when designing a home. By using this information you can enable your home to be shaded in the summer, and receive warming sunlight in the winter by adjusting the amount of overhang your roof extends over the walls of your home. As the sun moves throughout the day and throughout the year, continual measurements will be needed to track its path.
Place the cardboard box outside at the desired location for measurement, receiving direct sunlight. Ensure the top of the box is perfectly level by checking with a spirit level and adjusting as necessary by propping it up with books or anything else.
Stick the pencil into the middle of the top of the box, with exactly 5 inches exposed, perfectly vertical and checked with the spirit level.
Measure the length of the shadow cast by the pencil onto the top of the box. Measure the length of the shadow in inches.
Divide the height of the pencil (5 inches) by the length of the shadow. For example, if the shadow was 10 inches long, 5/10 equals 0.5.
Find the tangent of this angle by pressing the "shift" key on your calculator followed by the "tan" key. You need to find the inverse tangent of 0.5. On most scientific calculators you will need to enter the following sequence to get the answer: 5 ÷ 10 ="shift" "tan" =. In this case you would get at answer of 26.57, this is the angle of impact the shade makes with the surface in degrees.
To utilise this data for overhang construction in a home, determine the difference in sun angle in summer and winter, and increase the overhang length (in the above example this was the length of the shadow) enough to block out the sun in summer, but small enough to allow sun in during the winter, where the pencil height would represent the height of a window.