Compound angle calculations

Does anyone know the formulas I need to calculate compound angles?

Here's the scenario I have. My customer wants to put solar on their roof but their roof is facing E-W. This orientation gives them a 76% efficiency and they need 80% to get the grant for their project. They want to tilt the panels to get better efficiency from them. So here is what I"m trying to calculate:

Their roof is facing 270 degrees and has an 18 deg pitch. What I want to know how to calculate is what angle will the panels be facing (both azimuth and tilt) if I tilt them 20 degrees towards south (180 deg). The southern edge will be flush with the roof and the northern edge will be the edge that is up off the roof.

The next thing I need then is for inter-row shading. I can calculate it when it's on the flat but adding the other angles into it makes it a bit more complicated because the corner that is highest in the first row casts a longer shadow on the lower portions of the next row of panels.

Thank you,

-Michael

Comments

  • Solar GuppySolar Guppy Solar Expert Posts: 1,962 ✭✭✭
    Re: Compound angle calculations

    What is your efficiency based on?

    PVwatts for Pittsburgh as an example of a 1kw array, 15 deg tile

    East South West
    965 1080 975 or about 89% of due south

    Forget the idea of offset mounting, cost a fortune and look the hell
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    I ran the pathfinder data through the program and there is some shading which cuts the efficiency to 78% optimum. To get the grant you need at least 80% efficiency. To do it with out the angle isn't an option for them.
  • mike95490mike95490 Solar Expert Posts: 8,569 ✭✭✭✭✭
    Re: Compound angle calculations

    Jack up the house and turn it, till the roof is aimed right.

    Or consider a carport with a solar roof. Or garden shed. Or a pole mount.

    I saw a city septic plant with odd racked solar arrays, looked like heck.
    Powerfab top of pole PV mount | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
    || Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
    || VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

    solar: http://tinyurl.com/LMR-Solar
    gen: http://tinyurl.com/LMR-Lister ,

  • Solar GuppySolar Guppy Solar Expert Posts: 1,962 ✭✭✭
    Re: Compound angle calculations

    what is causing the shading? How can it be shaing both east AND west, one should be better than the other. is it required to use path finder data for the grant? Did you run pathfinder for both East and West?

    Offset racking is something I would never recommend or install, ever
  • CariboocootCariboocoot Banned Posts: 17,615 ✭✭
    Re: Compound angle calculations

    Pole in the ground + track mount. No alignment problem.
    May not be possible, but should be considered.

    Compound angle calculations are the bane of carpenters everywhere. Even the charts given for setting saws say "approximate" on them and you have to try a few times before you get it right.

    Any sort of complex "raised" mount is bound to have structural issues and may present a greater 'sail' to the wind.
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    I attached a model of the home. The orange line points to true north. I just need to calculate the off set angles to enter into pathfinder.

    Yes they want pathfinder data for the grant.

    I don't like the offsets either but they are insisting on maximizing their roof space. I'll do them for them as long as they perform if they're insisting on it.

    Thanks,

    -Michael
  • Solar GuppySolar Guppy Solar Expert Posts: 1,962 ✭✭✭
    Re: Compound angle calculations

    If I understand your model, you can maximize the array but using the East roof, it has no shading and will out perform the offset array as it will never be shaded and can have many more panels ( this assumes the West is where the addition is ), run the calculations for yourself
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations
    Pole in the ground + track mount. No alignment problem.
    May not be possible, but should be considered.

    Compound angle calculations are the bane of carpenters everywhere. Even the charts given for setting saws say "approximate" on them and you have to try a few times before you get it right.

    Any sort of complex "raised" mount is bound to have structural issues and may present a greater 'sail' to the wind.

    Ground is not an option because the surrounding homes and trees create an even greater shading issue.

    I'm not looking at doing fancy cuts, just a single tilt angle to the south.

    What I'm looking for is the final azimuth and tilt angle that the panel is facing. So in my mind I'm thinking that a 18 deg tilt west and an 18 deg tilt south would produce an azimuth angle of 225, but I'm not positive and I don't have a clue on what formula I could use to calculate it. I need the azimuth and tilt calcs so I can enter it into pathfinder to get the orientation efficiency numbers for the grant.
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    Not sure the east side would work because of the shading. Here is the pathfinder report for the photo at the peak.
  • icarusicarus Solar Expert Posts: 5,400 ✭✭✭✭
    Re: Compound angle calculations

    Without doing the calcx, I agree with SG, fill the SW roof facet with as many PV panels as you can fit and you will probably end up with more harvest net/net at a cheaper cost and with far less hassle and it would look better. With Pv costs as low as they are, it would be my guess that you could by another panel for the cost of tilting any given panel. Also consider the engineering costs of installing them on a skew.

    Tony
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations
    If I understand your model, you can maximize the array but using the East roof, it has no shading and will out perform the offset array as it will never be shaded and can have many more panels ( this assumes the West is where the addition is ), run the calculations for yourself

    The ridge of the main roof points to true north-south. With no shading at all an east-west roof with 18 deg pitch in our area will be 84% efficient. Just a few trees kills that last 4% efficiency that they need.
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations
    icarus wrote: »
    Without doing the calcx, I agree with SG, fill the SW roof facet with as many PV panels as you can fit and you will probably end up with more harvest net/net at a cheaper cost and with far less hassle and it would look better. With Pv costs as low as they are, it would be my guess that you could by another panel for the cost of tilting any given panel. Also consider the engineering costs of installing them on a skew.

    Tony

    That's what I would do if it wasn't for the grant wanting 80% efficiency. Pathfinder calculates it at 76% if I do it flat.
  • Solar GuppySolar Guppy Solar Expert Posts: 1,962 ✭✭✭
    Re: Compound angle calculations
    The ridge of the main roof points to true north-south. With no shading at all an east-west roof with 18 deg pitch in our area will be 84% efficient. Just a few trees kills that last 4% efficiency that they need.

    Doesn't make sense ... since your panels don't fill the entire roof ( East ) you can shift the arrays to keep out of what small areas of shading there is ... you can also knock down a tree or two, much lower cost than offset mounts
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    They're in luck, I just filled out the grant calcs and it takes the average efficiency of the entire system not just the one array. The total calc in the grant app comes out to 82%. They're going to be very happy with the whole west roof filled. 7.38k should make them quite happy.

    I'd still like to know the formula though for calculating the compound angles if anyone knows what it is.

    Thanks for your help guys,

    -Michael
  • mike95490mike95490 Solar Expert Posts: 8,569 ✭✭✭✭✭
    Re: Compound angle calculations

    Are you using 2 inverters on that install ?? ( one for each roof direction)
    Powerfab top of pole PV mount | Listeroid 6/1 w/st5 gen head | XW6048 inverter/chgr | Iota 48V/15A charger | Morningstar 60A MPPT | 48V, 800A NiFe Battery (in series)| 15, Evergreen 205w "12V" PV array on pole | Midnight ePanel | Grundfos 10 SO5-9 with 3 wire Franklin Electric motor (1/2hp 240V 1ph ) on a timer for 3 hr noontime run - Runs off PV ||
    || Midnight Classic 200 | 10, Evergreen 200w in a 160VOC array ||
    || VEC1093 12V Charger | Maha C401 aa/aaa Charger | SureSine | Sunsaver MPPT 15A

    solar: http://tinyurl.com/LMR-Solar
    gen: http://tinyurl.com/LMR-Lister ,

  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    Not sure yet, I'm going to talk to the customer about it. Either 2, 11, or 36 inverters ;)
  • Green Building SolutionsGreen Building Solutions Registered Users Posts: 24
    Re: Compound angle calculations

    Ok I think I have all the calculations figured out. I sat down with a friend of mine and this is what we came up with.

    Q. 40x65 panel is on a roof in portrait mode with an 18° pitch that faces 270°. The panel is tilted 22° towards true south. What is the azimuth and the tilt of the panel.

    A.
    sqrt(40^2 + 65^2) = diagPanel = 76.32

    Base and height of southern triangle
    cos18*65=Base1 =61.818
    sin18*65=Height1 =20.09

    Height of eastern triangle
    sin22*40=Height2=14.98

    Height of diagCorner (the highest corner)
    Height1+Height2=Height3 = 35.074

    Tilt of panel
    90(cos-1(Height3/diagPanel)) = 27.36

    Base of diag
    cos(Tilt) * diagPanel = 67.78

    Orientation of panel

    270-(Base1/diagBase * cos-1) = 245.7 deg
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