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Ron,

       The method you describe is the one I used in this post. It is convenient in that, by assuming the altitude around noon is quadratic in time, least-squares regression has a closed form solution. It has a number of disadvantages however

• It works well only for relatively short intervals around local noon.
• The quadratic fit becomes worse as the Sun’s noon altitude increases.
• It does not account for the Sun’s changing declination in shifting the time of peak altitude. This effect then needs to be accounted for separately.
• It is a 3-parameter fit to a problem with 2 free parameters.

In order to address all of these limitations I modified the method to do a least-squares fit to the true formula for the altitude as a function of time and described it here. The 2-parameter minimization is easily done in Excel using “Solver”.

Regards,

Robin Stuart