inter-row shading [RE-wrenches]

[Bill Brooks]

William and wrenches,

I was a little confused about this issue for a while myself until I looked
at it more closely. The tools you have provided are helpful, but there may
be some need for refinement to keep people out of trouble.

The simple solution is to avoid shading at noon on December 21 and that
turns out to be an okay way to look at it. However, we know that the sun is
lower in the sky the rest of the day. The proper answer is to do a detailed
computer analysis and come up with the best ratio of ground cover to shading
for the year. That will differ throughout the U.S. depending on prevailing
weather patterns and such. The quick answer is to not allow inter-row
shading after 9am and before 3pm (up to 40 degrees north latitude), but this
can be overly restrictive in higher latitudes. At higher latitudes, like 50
degrees north, a 10am to 2pm window is more reasonable.

For south-facing arrays, there is a 3-D solution that includes both the
altitude angle and an azimuth angle. The equation is as follows:

Spacing = cos(azimuth angle)/tan(altitude angle)

Where the spacing refers to the ratio of distance between rows to the height
difference of southerly row to the bottom northerly row. The reason the
cosine of the azimuth comes into play is that the altitude angle is
foreshortened by the azimuth angle when you are off of due south. The worst
case scenario is usually the shading that occurs around 10:00 am or 2 pm in
the winter. 

If the worst case that you will allow is 20 degrees altitude angle and that
happens when the sun is 30 degrees east of south, then the answer is as
follows:

Spacing = cos(30)/tan(20) = 2.4 times the height difference.

Inter-row shading becomes much worse at higher lattitudes as expected. If
you only want to allow shading when the sun is below 10 degrees above the
horizon at 44 degrees latitude (New England), the solution would be:

Spacing = cos(40)/tan(10) = 4.3 times the height difference.

This simple solution works for south facing arrays. If the array is facing
other than south, than the azimuth angle is not used. It would be the
difference between the sun's position relative to the direction of the PV
array. (Example: if the sun is at an azimuth of 40 degrees west of south and
the array is facing 25 degrees west of south, the apparent angle to the
array is 15 degrees).

I hope this is clear. Let me know if you have any suggestions to make this
more clear.

Bill.

Bill Brooks, PE
Brooks Engineering

> -----Original Message-----
> From: William Miller [mailto:wrmiller at charter.net]
> Sent: Saturday, January 27, 2007 3:18 PM
> To: RE-wrenches at topica.com
> Subject: Re: inter-row shading [RE-wrenches]
> 
> 
> Wrenches:
> 
> Here are two ideas for solving the inter-row shading issue:
> 
> 1. Set up the south row (in the northern hemisphere) of modules and place
> your Pathfinder behind it.  Move up the roof (or north in the field) until
> your desired time and date becomes free of obstruction.  Extend a line
> from
> the top of the obstruction through your pathfinder to the roof surface to
> find where the second row should start.


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