RegGuheert wrote:I'm helping a friend install a PV array on his workshop. He wants to mount the array on a 4:12-pitch roof which faces about 30 degrees north of West. In order to get the panels to face South, the intent is to mount the rails at *some* oblique angle to the roof and then use an elevation kit to raise the backs of the panels.

OK, I'm going to work this out as I type, so bear with me.

I think the way to approach this is to use vector math on the vector orthogonal to the face of the panels. Vector length will be arbitrary, as we are only interested in direction.

So let's have the x-axis point east, the y-axis point north, and the z-axis point up.

If the 4:12 pitch roof faced due south, the orthogonal vector would be (0,-4,12) or (0,-1,3).

Since the building is turned 120 degree CCW from above, this become (-sin 120, -cos 120, 3) = (-sqrt(3)/2 , 0.5, 3)

Say you want the panels to face south at an elevation of 40 degrees. That vector would be (0,-sin 40, cos 40).

The cosine of the angle between the vectors is their dot product divided by their lengths. The angle is

arccos((0 + cos120 sin40 + 3 cos 40)/sqrt(10)) = arccos(0.625) = 51 degrees.

So you would need to an elevation kit that would rotate your panels 51 degrees, not sure if that is practical. We still need to find what direction to run the rails.

The rails would need to run perpendicular to both the pre and post rotation orthogonal vectors, i.e. perpendicular to both (-sin120, -cos120, 3) and (0, -sin 40, cos 40). That would be in the direction of their cross product. So the direction is given by

(-cos 120 * cos 40 - 3 * (-sin 40), 3 * 0 - (-sin 120) * cos 40, -sin 120* (-sin 40) - (-cos 120) * 0) = (2.31, 0.766, 0.557)

If the rails ran horizontally across the roof, their direction would be (cos 120, -sin 120, 0). So the angle between this and the desired rail direction is

arccos( (2.31 * cos 120 - 0.766 * sin 120 + 0) / sqrt (2.31^2 + 0.766^2 + .557^2) ) = 137 degrees.

Since the rail directions are only defined upto +-1, this is really 180 - 137 = 43 degrees. I haven't calculated whether that's CW or CCW, but from the roof it should be obvious which way to go.

The upshot is that for the inputs of a 1:3 slope, 120 degrees off south, and a desired south elevation of 40 degrees, you need to rotate the rails 43 degrees from the horizontal on the roof, and you need to elevate the panels 51 degrees relative to the roof. If I didn't make any calculation errors.

You could easily check this with a very small model. For other values of the inputs, repeat the calculation above substituting the new inputs.

If you have more than one row of panels, you will have to figure out how far apart to space the rows to avoid shading.

Cheers, Wayne