Tracking Timelapse

I've put the below primary mirror offset compensation calculations in place, and the rig it tracking well! I made a little timelapse with my webcam behind a pair of sunglasses to prevent overexposure outside.

Tentative Solution to the Offset Mirror Problem

After tackling the cad model in a different way it became clear that the tips of the incoming ray vectors all lay on a circle offset from the circle traced by the centre of the elevation mirror. Knowing this and using some similar triangles I came up with these two equations:

a_z = sin^-1(sin(o_ff)/cos(e))

e_m = tan^-1(tan(o_ff).tan(e)/(sin(a_z) + tan(o_ff).cos(a_z)))

where :

a_z            =             additional azimuth angle added by primary mirror

e_m           =             required elevation of the primary mirror

o_ff           =             offset of the primary mirror from centre

e             =             calculated elevation of the sun

Now the required machine position can be calculated from the elevation and azimuth angles of the sun.

The Source of the Error

Because of the way the primary mirror is offset to prevent shadow being cast onto it from the secondary mirror, it turns out a few complications occur. The adjustment of the primary (elevation) mirror angle effects the azimuth alignment because the reflection plane is not vertical (as it would be if both mirrors were in line). To solve this I need to be able to calculate the two angles marked 'x' and 'y' from the elevation angle E and the mirror offset (currently 18.4deg). I know that the angles 'a' are equal (this is the path of a ray in the plane of reflection).

I have had a go at this but so far am struggling with the derivation. I assumed that the solid lines were of known length (1 for convenience) but this may not be necessary. If anyone feels inspired please give it a crack and let me know how you get on!