To shade the entire south wall at noon during the summer solstice with a solar angle of 9 degrees, the minimal overhang required is approximately 1.7 feet, ensuring effective shading.
To determine the required overhang of a roof for shading the entire south wall at noon during the summer solstice, we can use the concept of the solar angle and shadow analysis. During the summer solstice, the sun is at its highest point in the sky, creating a small solar angle. The challenge is to design the overhang in a way that prevents direct sunlight from reaching the south wall.
The solar angle (θ) can be calculated using the formula:
Theta equals 90 degrees minus the elevation angle of the sun.
Given that the elevation angle of the sun during the summer solstice is 81 degrees, the solar angle would be:
Theta equals 90 degrees minus 81 degrees, which equals 9 degrees.
To provide full shading on the south wall, the overhang should be designed to cast a shadow at least as far as the south wall height. The minimal overhang (d) required can be calculated using the tangent of the solar angle:
The tangent of theta equals overhang divided by wall height.
Given that the tangent of 9 degrees is a small angle, the overhang can be approximated as:
The overhang is approximately equal to the wall height multiplied by the tangent of the solar angle.
So ,
overhang = 11 * tan 9 = 1.7 feet