Thursday, December 2, 2010

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:

az = sin-1(sin(off)/cos(e))
em = tan-1(tan(off).tan(e)/(sin(az) + tan(off).cos(az)))

where :

az            =             additional azimuth angle added by primary mirror
em           =             required elevation of the primary mirror
off           =             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.

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