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    Re: Compass correction using sunrise
    From: Al Stewart
    Date: 2022 Jun 27, 14:11 -0700

    Hi Francois,

    I am happy to assist!

    The tabulated values for Sunrise shown in the almanac are rounded to the nearest minute, which are good enough for a navigator to estimate when he should be on deck to make observations... of course he should be in place a few minutes in advance.

    For precision, I use the attached spreadsheet, which uses the spherical trig equations to calculate computed altitude (Hc) and True Azimuth (Zn) using values entered in the the "green" fields, beginning at the top row and work your way down... let's give it a go!

    Beginning with your estimated time of Sunrise, 04:08:00 LMT = 04 (H), 8 (M), 0 (S) in the LMT fields, and a value of "4" in the LMT--> UTC field.... 

    Entered your precise Latitude and Longitude OK...

    Consult the Nautical Almanac (Daily Pages) for 16 June 2022 to extract Sun GHA and Dec at 08h UTC, "d" correction and Semi Diameter... entered those values OK...

    The GHA change in 1 hour is 15 (D) 0 (M) 0 (S) for Sun & Planet calculations, OK...

    There is a blank green field to allow 360° increment correction for LHA, which is not applicable in this case so is left blank...

    The spreadsheet outputs (in gold fields) are computed altitude (Hc) and True Azimuth (Zn) using spherical trig formulas (note d = Declination, L = Latitude)

    sin Hc = (sin d x sin L) + (cos L x cos d x cos LHA)

    cos Z = (sin d - (sin L x sin Hc)) / (cos L x cos Hc) 

    and for Northern Latitudes, with LHA between 180° and 360°, the true compass direction or True Azimuth (Zn) = Z.   

    So, for that instant in time 04:08:00 LMT, we get Hc = - 0° 53.4' and Zn = 052° 11.1' (T); that means at that instant, the CENTER of the Sun is still 53.4' BELOW the theoretical horizon... 

    If we gradually increment the LMT time entries ahead from 04:08:00 LMT, and observe the Hc, you will see that Hc becomes zero at 04:14:43 LMT; at that instant, we would actually observe the Sun to be completely above the horizon by eye (due to refraction), such that its bottom edge / Lower Limb appears ~ half its diameter above the horizon. This is the instant when the Sun observation is used for compass checks by Amplitude, which again is a little after the instant of Sunrise which is when the top edge / Upper Limb of the Sun first becomes visible above the horizon.

    Yours aye,

    Al Stewart



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