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.