Solar Incidence Analysis

Performing a solar incidence analysis , an analysis of the intensity of solar radiation on the surface of a building, is increasingly becoming common practice in the design of overall building form as well as customized surface devices such as frits and fins. Solar radiation varies in different parts of the world as well as on different surfaces of the same building. Radiant energy from the Sun strikes surfaces on the Earth at different angles of incidence , angles made between the Sun vector and the normal vector to the surface. This varies within any day as the Sun's position traces its path in the sky, and within a year as the daily average altitude changes. At the equator where the Sun passes almost directly overhead, the intensity of light and heat received on horizontal surfaces is usually much greater than on vertical surfaces. At higher latitudes, this begins to change as the Sun is much lower in the sky and the intensity of radiation on vertical surfaces is much more than on horizontal surfaces.

To measure the radiant intensity at any position on a building surface, let's assume that the surface has a constant radiance that is independent of the viewing direction. In this simplified situation, the radiant intensity is governed by Lambert's cosine law, which states that the intensity of radiant energy is directly proportional to the cosine of the angle of incidence. This can be written as

<math> I_S = I_n \cos{\theta}</math>

For normal incidence <math> \theta = 0</math> so <math> \cos{\theta} = 1 </math> and <math> I_S = I_n </math>. This quantity <math> I_n </math>, called normal irradiance , is often measured and recorded in such weather files as EPW files on an hourly basis. For all other angles, <math> \cos{\theta} </math> is less than 1 and <math>I_S </math> is reduced. Thus, even though a homogeneous planar surface viewed from any position will seem to be uniformly illuminated (constant radiance), the intensity of radiation on that surface varies as the Sun vector moves from normal to parallel to a surface.

Let's start by computing radiant intensity on a planar surface. We will build up starting from the simple case of a fixed Sun vector and a fixed direct normal irradiance which is equivalent to fixing a geographic location at a fixed time to the case where annual data is brought in and aggregated. We will then perform an aggregated solar incidence analysis on an entire building surface.

Solar Incidence Analysis on a Plane

A planar surface is determined by a single normal vector so performing a solar incidence analysis on a plane amounts to being able to track the movement and normal irradiation of the sun. What is needed to track the movement of the sun is an input of a fixed geographic location (determined by a latitute, longitude and time zone) and an instant (given by a date and time) which results in a vector pointing to the position of the sun. Since the distance from Earth to the sun is on average 150 million km, a Sun vector at a fixed location and instant as seen from any point on a plane on Earth will be the same, no matter how big the plane. For this purpose, we have created a solar geometry module which performs the computation of a Sun vector given inputs of latitude, longitude, date and time. The normal irradiation of the sun is a measured quantity captured in such data files as the EnergyPlus Weather (EPW) files format on an hourly basis.

Let's begin with the simplest case of a fixed location and instant where the plane of interest and normal irradiation are also user inputs. Then all that is needed is to access the functions within the solar geometry module and then to calculate the angle of incidence. A simple visualization of the resulting intensity of radiation on this plane in color as well as in the length of the normal vector is also given alongside the actual value.

Aggregating Data

Up to this point, the normal irradiation has been a hard-coded input so unless the user is changing this value for every location and instant, the current computation is really only showing what the Sun's path is. To get an accurate picture of how the intensity of solar radiation varies over the course of a day as well as for different geographic locations, we need to access the normal irradiation data captured within the EPW files. It makes sense to also take advantage of other data in the EPW file such as location parameters, so that the only user inputs becomes the path for the EPW file itself and the plane of interest. A more refined version of the code that we just presented could introduce two functions as follows:

function extract data from EPW file:
    input: path of EPW file
    output: a dictionary with epw data (location and normal irradiance)

function calculate radiant intensity for a fixed location and  instant on a planar surface:
    input: a plane, instant, epw data 
    output: the value of radiant intensity on the plane
    split the string according to the tab character
 

Now that we can read in data, we are faced with the unwieldy situation that if nothing further is done, there is a different radiant intensity for each of the 8760 hours of the year. One way to get a quick read on how the radiant intensity varies with planes at different orientations is to aggregate this data. Many ways of aggregating have been done and the appropriate choice varies with the application at hand. Some simple examples of aggregation over time are yearly maximum radiant intensity, yearly averages, seasonal maximum/averages. In the diagram below, results of an aggregated solar incidence analysis on the same plane are shown.

Solar Incidence Analysis on a Building Surface

Building upon the code developed to compute an aggregated solar incidence analysis on a single plane, we can now bring in a building geometry captured as a collection of planes (such as a mesh) to perform an aggregated solar incidence analysis on an entire building surface. Since we already have functions that extracts the data from the epw file and which calculates the radiant intensity for a single plane at a fixed location and instant, the only work is to to perform this calculation on every plane that makes up the building surface.