How to Calculate Solar Shading

As the sun sits higher in the sky in summer than in winter, simple mathematical calculations can help us devise an appropriate length of overhang a roof protrudes over a window to allow the window to be shaded during the hot summer, and allow warming sunlight in during the colder winter. By simply planning the design of a home or other structure can drastically reduce heating and cooling costs. Measuring the angle of shade in your particular area is easy with a little trigonometry. Remember that continuous measurements are necessary throughout the day and year.

Pencil
Cardboard box
Ruler
Spirit level
Scientific calculator

Instructions

- 1
  Place your cardboard box outside in direct sunlight, and ensure the top of the box is perfectly level by checking and adjusting if necessary with a spirit level.
- 2
  Stick your pencil into the center of the top of the box with 5 inches of it exposed above it. Check that the pencil is perfectly vertical and perpendicular to the box with your spirit level.
- 3
  Measure the length of the shadow created by the sun on the surface of the box. Ensure this measurement is taken in inches.
- 4
  Divide the height of the pencil (5 inches) with the length of the shadow. For example, if the shadow cast was measured to be 8 inches, 5 ÷ 8 = 0.625.
- 5
  Find the inverse tangent of the quotient (answer) from Step 4. In the above example, enter into your scientific calculator, "5 ÷ 8 = "shift" "tan" =." You should get an answer of 32.00. This is the angle, in degrees, at the moment of measurement that the sun impacts the pencil and box.
- 6
  Determine the average angle of impact the sun makes at your location in summer as well as in winter, and adjust the overhang of your south facing roof over a window (in our equation this was represented by the shadow on the box) so that it will shade the entire height of the window (in our equation this was represented by the height of the pencil) in summer, while letting the sunlight in during the winter when the sun sits lower in the sky. This will help to passively heat your home in winter, and help with cooling in summer, through a south facing wall in your home.

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