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    Re: Were Short methods really Short?
    From: Stan K
    Date: 2016 Aug 8, 07:40 -0700


    These are copies of two messages I sent last night that apparently did not make it through.

    I've been out of touch for the last few days.  I just got back and saw your message.  Without working through the numbers, which I will probably do later today, a few things come to mind:
    The app that give the sun's azimuth at sunrise probably gives the azimuth when the upper limb is on the visible horizon.  Bowditch Table 27 give the azimuth of the sun when its center is on thecelestial horizon.  (Table 28 is used to correct this to the visible horizon.)
    I suspect that these considerations might account for the discrepancies.
    I just confirmed that, for your example, the azimuth of the sun when its upper limb is on the visible horizon is 62.2569...º, rounding to 62.3º.  The azimuth of the sun when its center is on the visible horizon is 62.0937...º. rounding to 62.1º.
    Another thing I failed to mention is that you used the closest latitude and declination available in Table 27.  Had you interpolated both you would have gotten 28.56038º.  The Table 28 correction is -0.7º.
    Using the rounded values (might as well, since Table 28 values are rounded):  62.3 + 28.6 - 0.7 =  90.2º, much closer to 90º than 28° 36' +  62°18' = 90º54' or 90.9º.  (Using the unrounded values results in something closer to 90.1º, even better.)
    Does this work for you?
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