The shape of shade: Understanding the relationship between an obstruction’s height vs. distance

Pop quiz: say you have a tree that is shading your array–then you make it 20 ft taller, while also moving it 20 ft farther from the roof. Are you better or worse off? It turns out that the shade losses will usually drop–and this phenomenon is one of the most commonly misunderstood factors that we hear from designers.

Understanding the shape of shade

Many people think the two trees will cast equal shade on the array. However, the impact of changing an obstruction’s height and/or distance vary greatly based on the relative location of the object versus the array. As can be seen in Figure 1, adding distance between the tree and the array will reduce the shade loss more than reducing the height would. For example, note that when a tree’s height grows from 50 ft to 70 ft, the shade impact can be more than offset if the tree is just 10 ft farther away from the solar array.

Figure 1: Shade loss values based on height of object and distance from array

Said differently, a taller tree that is farther away from the array creates less shade than a shorter tree that is closer to the array. You might have a really scary looking tree that is 100-ft tall, but if it is 70 ft from the array, the shade losses can be negligible.

To understand why this is the case, it helps to look at the shade loss from an object in a more abstract sense. Let’s examine what happens when we simulate a large 100-ft tower surrounded by modules on all sides. Only the modules closest to the tower receive significant shade loss (a few with shade losses above 50%). By the time you are 30 ft from the tower (about six rows of modules) the shading losses drop to under 10%.

Figure 2: 10% shade threshold next to 100-ft tower

Modules farther than 30-ft away are only impacted slightly by the tower, with shade losses on the order of 1 to 4%.

Figure 3: Shaded modules at 50% shading, 10% shading and 1.7% shading from 100-ft obstruction

In essence, the shade loss from an object nearly resembles a 1/x curve: it’s very high close to the object, but falls quickly before flattening out at low values.

Figure 4: Curve showing y=1/x

Real-world manifestation

This concept of relative shade loss comes up all the time with HelioScope users. Most commonly, somebody will design a system near a tree that is 80 100-ft tall. Yet the shade losses from the tree will only be 2 to 3%, sometimes even less. As we troubleshoot, it turns out that the imposing tree is also 100 ft away from the array–and that distance effectively neutralizes the height. An oak in the neighbor’s property is less daunting than a nearby sapling.

Ultimately, the main takeaway here is that our intuition is often wrong with respect to how much shade we should expect from an obstruction. Based on our conversations, it seems like people often focus entirely on the height of the tree or building, and have difficulty factoring in how far away it is. As a result, we are often more hesitant to design around tall obstructions – but if you just run the analysis, you might be surprised at how modest the shade impact is.

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