- SECS, Chapter 7, Applying the Angles to Shadows and Tracking
Here, we are going to work through a problem of plotting critical points of shading onto an existing sun path diagram. Keep in mind that we will use the plots that you developed from the University of Oregon Solar Radiation Monitoring Laboratory in the "Try This" section on the previous page.
Here, I am using a program called Skitch to draw over the top of my PDF files. There is a 30-day free trial of the editing software if you would like to use it to digitally mark up your documents. Otherwise, I recommend that you print out your work, draw on the print directly with a pen, and then take a snapshot of the edited image with your phone or scanner to upload.
Quick review of the Charts:
First, we will go over the key features of the orthographic plots with the arcs of six days plotted out for the first half of the year.
Second, we can compare the key features of the orthographic plots to the polar plots, again with the arcs of six days plotted out for the first half of the year. You should notice the similarities (East is on the left, solar time is represented, the same location is plotted), as well as the distinct differences (the June and December arcs are "flipped").
How to integrate shading as an overlay
Now, we need to add an additional layer of information to the plot. I'm going to talk through the addition of critical points on the sun chart, followed by connecting those points and shading the areas correctly. In each of the following examples, we will use orthographic projections, but there is no reason why you couldn't use polar plots instead.
NoteWe are not plotting what the shadow "looks like." Instead, we are plotting the times over the course of a year (or half-year) for which a shadow exists on our receiving points of interest. We know that the actual shadows on a building are rectangular in shape (or have straight edges). However, the plot of the times in which shading occurs will not necessarily be rectangular.
The first example will come from the textbook. We will be plotting shading relative to a single receiving point: X, with three critical points of shading (A, B, and C).
In the next example, we will look at setting up the problem to assess a PV array shading problem. Our intent is to plot shading relative to multiple receiving points: A, B, and C, with three critical points of shading (1, 2, and 3). The result is nine values for altitude coordinates ( , no subscript) and nine values for azimuth coordinates ( , no subscript).
You will notice how the horizontal surfaces of the building that create shadows are transposed to the projection as an arc, not as a horizontal line, while the vertical surfaces remain vertical. This has to do with the manner in which spherical data is distorted in an orthographic projection. Hence, the plot of a building shading a point on a window will look a lot like a slice of bread, flat on the sides with a soft curve across the top. The same will be found for this example, where the receiving points A, B, and C are shaded at different times by critical points 1, 2, and 3.
Next, we will be interpreting our results, and inputting the shadow data into SAM.