Shadow length question?

I’m designing a solar array for a strangely designed house. I need to find out how to calculate the furthest south a shadow will travel in a given day. There will be panels lined up behind one another and i want to make sure no shadows from one line of panels hit the ones behind them, but I also want to use as much roof area as possible. Initially I was under the impression that the shadow would travel the furthest southwards at noon but recently discovered this to not be true. How do I find this out?