Calculating % loss of efficiency from roof orientation changes

[Davehewy]

I am trying to build some open source software which will help people with understanding and calculating solar panel installations. I have worked out how to calculate the most part of the data based on angle, latitude and longitude, and average recorded calculations.

But i'm struggling to work out the effect of changing the orientation of the install surface away from the optimum which we know to be SOUTH in the northern hemisphere. I wanted to be able to show methodology behind a calculation that would show the effect of perhaps having a NORTH facing surface rather than a SOUTH facing surface.

Any help would be hugely appreciated.

[Naptown]

I use Solar pathfinder assistant which takes this into account. I believe the algorithms are based on the PV watts models