Basically I am trying to find the optimum angle at which a solar panel should be installed by using vectors. I have done some research but found it a bit confusing , so basically I haven't got very far. What I did find was this formula which tells me that to calculate the total amount of sunlight reaching the panel ($S_{module}$), the solar incident ($S_{incident}$) must be multiplied by the dot product of the solar vector ($S$) and the normal vector of the panel ($N$). However I am not sure how to continue on from here (mainly because I don't know how to find an expression for the normal vector at any location on earth). What I want to achieve in the end, is find an equation which would give me the optimum angle of the solar panel at any latitude on earth.
This is how I started..
$$\begin{align} S_{ module }=&{ S }_{ incident }\ S \cdot N \\ &Since \left| S \right| =1, \\ &={ S }_{ incident }\left| N \right| cos{ \theta }_{ panel.elevation }\end{align}$$
Thank you in advance for your help!