Determining Module Inter-Row Spacing
In this article you will learn how to calculate the inter-row spacing for tilted or ground mounted PV systems. You may avoid potential shading issues and have the ability to increase the system size.
When designing a PV system that is tilted or ground mounted, determining the appropriate spacing between each row can be troublesome or a downright migraine in the making. However, it is important to do it right the first time to avoid accidental shading from the modules that are ahead of each row. This can lead to under-performing systems and angry customers. No one wants to have that. The same can be said about overcompensation too. Think of how many more kW’s you could have had. This article will get you started off on the right foot with a simple and fast process to get you out in the field faster with great results.
The first step in calculating the inter-row spacing for your modules is to calculate the height difference from the back of the module to the surface. To do that, follow this calculation below:
Height Difference = Sin (Tilt Angle) x Module Width
***Make sure you’re calculating in degrees, not radians***
In this case, I am using a SolarWorld module that has a width of 39.41 inches at a tilt angle of 15º.
Height Difference = Sin (15) x 39.41
Height Difference = 10.2” rounded down to 10”
To calculate the Module Row Spacing we need to hop over to http://solardat.uoregon.edu/SunChartProgram.php to determine what our Sun Elevation Angle is going to be. You will enter in your site's zip code or be more precise you should enter the latitude and longitude of the location for more accurate results.
When you get your results it will look something like this:
In this example, I picked a 9 AM to 3 PM window during the winter solstice for the worst case scenario. You may opt for a less stringent case to suit your needs. I chose this example because some utilities require the 9am-3pm window when offering rebates for customer owned PV systems.
From the chart, you see that I have highlighted this window and drawn a horizontal line out to the left of the chart to narrow in on the Solar Elevation Angle at those times. I estimate a 17º angle which I will use next to determine the Module Row Spacing using the formula below.
- Module Row Spacing = Height Difference / Tan (17)
- Module Row Spacing = 10 / Tan (17)
- Module Row Spacing = 32.7” rounded up to 33”
There you have it! The inter-row spacing between the trailing edge of the first row of modules and the leading edge of the next row needs to be 33”
We’re not done just yet and you’ll be glad you kept reading along…
The next thing we must do is account for the Azimuth angle and use that figure to apply that to another formula. Take a look again at the example below; you’ll see that I have drawn two vertical reference lines down from each time reference. The difference between South going in either direction turns out to be 44º and we will use this in the following formula to determine the Minimum Module Row Spacing!
- Minimum Module Row Spacing = Module Row Spacing x Cos (Azimuth Correction Angle)
- Minimum Module Row Spacing = 33 x Cos (44)
- Minimum Module Row Spacing = 23.7” rounded up to 24”
Hey, you just gained an extra 9” for every row you have in your system! On cramped roofs or large commercial systems that can make all the difference. Put another way, in this scenario we could potentially increase the system size by 27%! What do you think about that?
And one last thing….
This last calculation is just a bonus and can help you layout your array in CAD a bit easier. The following formula gives you the distance from the trailing edge of one row to the trailing edge of the subsequent row or your Row Width.
- Row Width = Minimum Module Row Spacing + Cos (Tilt Angle) x Module Width
- Row Width = 24 + Cos (15) x 39.41
- Row Width = 62”
Now go break out the TI-86 and put in some fresh batteries, I think you’ll enjoy figuring out the inter-row spacing for all of your tilted or ground-mounted PV systems. Have fun!