Photovoltaic Tutorial:

Optimum Array Orientation & Placement

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The golden hours of peak sunlight lie between the dotted lines of the two solstice suns, and between 9 a.m. and 3 p.m daily. This is known as the solar window. If any object -- be it on the roof or in the nearby surroundings -- should eclipse the sun where it shines on the array, the electricity output may decrease substantially.

How to Measure a Year's Worth of Shade by Hand

To predict shading over an array, the site assessor takes into account any obstruction, near or far, that can get between the sun and the array some time during the year. Naturally, obstructions located to the north of the array are of no concern. Also, shading that occurs outside the solar window of 9 a.m. to 3 p.m. daily is typically not counted against the potential kilowatt hour estimate. (It's common practice, however, to widen the window for the summer months.)

In a nutshell, a shadow will be cast across an array if an object's elevation or altitude angle is the same or greater than the sun's when they share the same compass bearing -- that is, from the perspective of the array. This bearing is called an azimuth angle.


Two measurements are necessary to find out if a tree or other potential obstruction will cast shade over your array at some point during the year. One is the elevation or altitude angle of the object. The second is it's compass bearing (factoring in magnetic declination).

Nearly all solar contractors use an expensive shading assessment device to determine the best placement for an array. A software app is included with both the Solar Pathfinder and Solmetric Suneye to help quantify shading, along with providing an estimate of annual insolation and sun hours.

You can, of course, compile the same intel using a few simple tools and data sets available for free on the internet. This is a useful skill to learn, not only for solar power applications, but for wilderness navigation, planning a farm or garden, astronomy, forestry management, surveying. Just keep in mind that many solar rebates and tax credits require you to submit a Pathfinder or Sun-eye report, so you may still need to rent or borrow one of these devices.

Here's a six-step guide to help you to get the job done for free:

Step 1: Generate a sunpath diagram online for your latitude.

A sun path diagram provides the track of the sun over a year's time for your local latitude and time zone. On the order form provided by the Univ. of Oregon online, you'll find several options to choose from. The first one to pick is "Look up location with a U.S. zip code." Next, select your time zone. Most of the default options that follow are OK, but to get a printout that's easier to read, select "Crop azimuth axis to fit plotted data," and "Crop elevation axis to fit plotted data."Also, in Step 5 you can add two title lines to identify your chart.


Diagram adapted from solardat.uoregon.edu.

The solid curving lines on the graph represent the sun's path on one day for each two months out of the year (e.g. April and August), except on the solstices, which represent one day. Although there's a white space between each curved line, it's assumed that the sun will gradually track through these spaces over the course of 30 days. The horizontal axis of the graph charts the azimuth angle (compass orientation), while the vertical axis charts the altitude angle.

The vertical dotted lines plot the time of day in relation to the azimuth and altitude angles. Remember, it's only between the hours of 9 a.m. and 3 p.m. that shading across an array is counted. For this particular chart, any obstruction located outside the compass range of 100 degrees (close to due east) and 265 degrees (close to due west) does not even need to be measured. The top azimuth scale, incidentally, uses the reference-to-due-south system.

Step 2: Next, go outside to the site of your potential solar aray and take compass bearing to determine the azimuth angle and width of each potential obstruction. Create a table with five columns before you start. The first column is for listing each of the obstructions by name. The second column is for the first bearing, the left side of the object. The third column is for the second bearing , the right side of the object. Don't forget to factor in declination in your readins, a process explained on Page 2 of this section.

As you size up potential obstructions, be on the lookout for deciduous trees. Since they lose their leaves in the fall, they'll have less shade impact between December and April. Make a note of this on your table, so you can shave off some of the tree's girth (graph-wise) in Step 4.

Step 3: Record the altitude angle of all the same obstructions.

For this task, you'll need a clinometer or theodolite. You can cobble together a makeshift tool If you have a protractor, a straw (for siting the top of the obstruction), Scotch tape, a foot of string, and a small weight, like a round rock. You'll find helpful links for this task in the caption below. This will give you a primitive form of theodolite, a device historically used in land surveys.

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Altitude or elevation angles are measured with an inclinometer (aka clinometer, theodolite, angle finder). The device is used for astronomy, surveying, and to measure trees. Several videos on Youtube (like this one) demonstrate how to quickly construct the device from simple materials. (Or you can try these online instructions.) After that, you can watch the next in the series to see how it's used. Remember, you don't need to find out the height of the obstruction, just the angle shown in the image on the left above. That's the altitude or elevation angle.

With your clinometer, stand or squat on the side (or at a corner) of your planned array, a few feet ahead of the nearest side facing the object. Let the rock dangle straight down so that it's exactly plumb to the ground. Sight the straight edge of the instrument so that one end is pointed at the top of the obstruction, the other end pointed down at the array. The idea here is create an invisible line running from the array to the top of the object, as the photo above left demonstrates.

With the protractor's rock plumb (dangling straight down), the string should now be lined up across the correct altitude angle on the curved ruler. Press a finger down on the string near the scale without moving it, and hold it taught while you turn the protractor to where you can read the angle. Record the result in the fifth column of your table. Then repeat the process for all the other potential obstructions.

Note: If you plan to rely solely on this data collection method to assess shading, you should repeat the entire series of measurements in each corner of the array, and at the center point as well. Create a separate table for each measuring location, then label them for easy reference -- e.g. "NE, SE, NW, SW, CENTER".

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If you know the height of an obstruction, and it's on level ground with your array location, you may be able to use the Pythagorean Theorum to compute its altitude angle. (The obstruction must likewise be perpendicular to the ground, rather than pitching forward or backward.) In addition to its height, you'll need to know the distance from its base to the array. Also, you'll need to know how much higher the array location is off the ground versus the object.

With this data in hand, first subtract the height of the array (off the ground) from the height of the object. If you look at the diagram below, you'll see why it's important to do this. For example, if you have a 40-foot-high obstruction and your array is 10 feet off the ground, your object height should be adjusted to 30 feet.


Using the Pythagorean Theorem to measure an altitude angle requires the height of the object, distance from the array, and a scientific calculator.

Now, divide the object's adjusted height by the distance on your calculator, then use the ArcTan key to get the altitude angle. Be sure to perform the division first, save the result in memory, then recall it after hitting Arc Tan. (You may need to hit "shift-tan" or "tan-1" keys if there's no arc tan option.)

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Step 4: On the sun path diagram, plot the coordinates for each potential obstacle.

The chart will tell you if an obstruction will eclipse the sun as it shines on the array. It will also tell you how long the shade will occur. As you can see, a sun path diagram is a simple line graph with X and Y axes. Plot each set of coordinates in pencil (i.e. the two azimuth measurements and one altitude angle), one by one. Mark the points near the axes lines on the chart. Now draw and fill in a vertical bar shooting up from the Azimuth axis. Once that's done, you can erase the horizontal line emanating from the Altitude axis.

Repeat the process for all the other objects you measured. And if you took readings from more than one location, repeat the tasks -- one sun path chart per location.


Each vertical bar represents a shading obstruction drawn onto a downloaded sunpath diagram. The altitude angle and compass bearings taken of the left and right edge of the obstruction are used to plot the top (vertical axis) and sides (horizontal axis). At the same time, the numbers written inside the squares are a rough estimate of the percentage of insolation dispersed around the course of the year. (They should total 100.) By adding the numbers where shade falls inside a square, you can get an idea of the shade impact at the array site. Note the negative numbers recorded at the bottom of the sheet. These represent the insolation cancelled out by each bar and add up to 21%. Clearly, it's the third obstruction from the right that's the big showstopper for this array placement. If it could be eliminated or reduced in some way (e.g. a tree pruning or removal), the location might otherwise be deemed a good one.

Step 5: Analyze the data to determine how much shading will occur.

First you'll need to hone in on the data that pertains to the solar window. To do this, draw a border along the following lines: the 9 a.m and 3 p.m. dotted lines between the uppermost and lowermost curved sun path line; and the curved sun path upper and lower lines, stopping at the 9 a.m. and 3 p.m. borders. Now you can use the graph paper squares to help you approximate a percentage of the solar window that's shaded.

You could start by taking the number of squares within the borders and dividing by 100 to allocate roughly the same percentage of insolation (i.e. sunlight on your array) to each square. For example, if you count 30 squares in the solar window, you could assign 3% to each one. Then you can add an extra 1% to the ten boxes closest to noontime, since that's when insolation peaks. Once you've allocated percentage values to the squares, you can make a tally of the shaded portion. Often, the bars you draw will only cover part of a square, which means that a 3% square that's half-covered translates into 1.5% worth of shading. Add up all the shaded percentages when you're done.

Next, if you made separate charts for multiple locations, you'll need to average the shading sums of all the charts. For example, if your percentage sums are 14 for NE, 5.5 for CENTER, 7 for NW, 8 for SE, and 10.5 and SW, first add them up (45), then divide by 5 (the number of charts) to get an averaged shade tally of 9%. That, in turn, indicates a 91% insolation value for your array.

Array shading is an aspect of system sizing that must be factored in to get a realistic expectation of system performance. It can be included as a derate when sizing the array. (Check here for a list of standard derate factors and how they're used.) More often, designers use the adjusted insolation value generated on a Solar Pathfinder or Sun-Eye report when it's time to count the modules needed.

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The chart is exerpted from a report by the Solar Pathfinder software and provides the month by month impact of shading on a proposed solar array. The photo on the right shows another module placement scheme designed to avoid a yearround obstruction - the chimney.

Step 6: Use one or more of the following remedies to correct and/or mitigate the problem of shading.

If your assessment produces more than 10% shading, you can take a variety of steps to improve that number. Moreover, any amount of shade -- even one percent! -- can cause a loss of voltage that affects all modules wired in the same series string. In addition to changing the placement or orientation of an array, you can and should try to mitigate its impact within the electric circuit . Here are the most common adjustments solar designers employ to address shading over an array site:

altenergy.com
A single-axis tracking system called SunSeeker is manufactured by Thompson Technology Industries. This solar solution is normally implemented where there's plenty of space to install scores of PV panels, like an apartment building, big-box retailer or college.Single and dual-axis tracking mechanisms are activated by sunlight, which change PV panel orientation so they'll follow the sun throughout the year. Tracking generally increases output by about one-thrid. A single axis rotates the azimuth direction, while dual-axis tracking does that and adjusts the array's upward tilt. Unfortunately, the extra components and required maintenance make tracking an expensive option for homeowners. And they may or may not effectively get around the shading.

If you're a homeowner considering a solar electric system, ask a professional contractor to help you figure out the most economical solution to the problem of shading. Sometimes an obstruction turns out to be not such a big deal -- for instance, a deciduous tree that loses all its leaves in the fall. If your chimney is in a bad spot, you may be able to avoid its shade by staggering your modules to avoid the shadow it casts, as shown in an earlier photo. Always consider creative ways to get around obstructions before abandoning a good spot with an ideal due south orientation and lots of space for modules.


The Solar Pathfinder, retailing at $260, comes with sun path charts covering a range of latitudes in both hemispheres. The curved lines are separated into 12 months, and crossed perpendicularly by hour lines. This makes it easier to allocate insolation. The device chart allows you to tally shading for each month, with the percentages divided by hour of the day. You can photograph the reading in the field, then load it into the software app (which costs an extra $190) for data crunching. Here's a sample report with the results. Alternatively, you can skip the app and add the numbers manually, then average the results of the different readings in the same manner described earlier in this section. To look it at a larger image of the photo above, see Page 8 of the user manual. Photo: SolarPathfinder.com.

Regardless, lost kilowatt hours due to shading cuts right to the heart of a solar PV investment and can extend payback time by a year or more. That's why it's essential to ask your contractor for copies of the data collected from a Solar Pathfinder or Sun-Eye survey. After reading this section, you'll be able to analyze the data yourself and suggest an alternative approach, if necessary.

For a look at a variety of photovoltaic simulators, calculators and software available to predict array performance, click here or here.

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