Go to this website to determine optimal angle for solar harvest.
Use one of these formulas to find the best angle from the horizontal at which the panel should be tilted:
If your latitude is below 25°, use the latitude times 0.87.
If your latitude is between 25° and 50°, use the latitude, times 0.76, plus 3.1 degrees.
If your latitude is above 50°, see Other Situations below.
If your latitude is below 25°, use the latitude times 0.87.
If your latitude is between 25° and 50°, use the latitude, times 0.76, plus 3.1 degrees.
If your latitude is above 50°, see Other Situations below.
I get Tilt angle = .76*39+3.1=32.7 degrees
Your roof is at 45 degrees and skewed from true south so your mounting plane for an array is out of plane with the roof 45-32.7=12.3 degrees in tilt and 180-158=22 degrees in azimuth. The 12.3 degrees in tilt would not be too hard to adjust for. Just mount the panel further from the lower part of the roof than the upper. The 22 degrees of Azimuth is another bigger challenge. If it was a west error instead of an east error you could probably just accept it as improved afternoon harvests. To adjust for this the panel now goes out of plane with the roof. The challenge is to find a set of mounting points, that can be built over that result in all mounting rails to be in plane but out of plane with the roof. That necessarily means all of the standoffs are a different length (assuming a regular spacing).
If you can lay the lower rail, on running east west but on a slant to the roof, then you just have to figure out the lengths of the opposite side (all the same) that give you the proper tilt angle referenced to N-S. The panels will be staggered, but as it is based on a small angle the spacing should not be too band. Not to try and make this less complicated than it is, obviously the installer would be trying to keep the mounting hardware to a minimum and so how many mounting points, how large the panel arrays are as well as the associated loading are all factors that come to play. There is another thread about "side tilt" and a picture of a staggered design similar to what your's would be.
I'm assuming the typical Solar Super Cuts installer is apparently not going to take the time to figure it all out. Being an engineer I would figure it out myself or get some software to do the design. I don't know what your skill set is whether you can balance all of the objectives and the constraints and come up with a workable plan that someone could bid to. I am pretty sure that the more you study it the more you will understand. There reaches a point however where a 3D Computer Aided Design (CAD) package is required.
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