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    Re: AN5954 bubble octant by Bausch and Lomb
    From: Gary LaPook
    Date: 2012 May 8, 02:20 -0700
    Let’s see how great a concern it should be if we use a median instead of an average for the
    altitudes and the time. Just by coincidence, exactly one year ago I took two series of nine shots
    each with my A-7 bubble octant to check its index error.
    (I have attached this as a pdf file because I can never get the format of a data table to come out right in email.)

    Here is the data:

    May 7, 2011. A.P. 34̊ 16.6' N, 118̊ 54.0' W. Center of the sun.

              23:46:00  35̊ 17'
                        14         06
                         29       09  
                         43       08
                        59       06
                  47:15        02
                       28       01
                       40  34̊ 58
                       58       52



    23:48:18  34̊ 51'
               31       48
               46       47
          49:04        41
                  21       39
                  37       33
                  51       33
            50:09        27
                  21       25


    The first series took 1:58 so the median time was 23:46:59 while the average time for the series
    was 23:46:58.4, a 0.6 seconds difference. The median altitude was 35 06' while the average
    altitude was 35 04.3' a difference of 1.7'.  Using the median time with the median altitude
    produced an intercept of 0.4 T; median time with average altitude = 1.3 A; average time with
    median altitude = 0.2 T; average time with average altitude = 1.5 A so the maximum difference
    was 1.9 NM.

    The second series took 2:03 so the median time was 23:49:20 while the average time for the
    series was 23:49:19.8, a 0.2 seconds difference. The median altitude was 34̊ 39' while the
    average altitude was 34̊ 38.2' a difference of 0.8'.  Using the median time with the median
    altitude produced an intercept of 2.4 T; median time with average altitude = 1.6 T; average time
    with median altitude = 2.4 T; average time with average altitude = 1.6 T so the maximum
    difference was 0.8 NM.

    If we combine both series into one 18 shot set then the total series took 4:21 so the median time
    was 23:48:10.5 while the average time for the series was 23:48:20.2, a 9.7 seconds difference.
    The median altitude was 34̊ 51.5' while the average altitude was 34̊ 51.3' a difference of 0.2'.
    Using the median time with the median altitude produced an intercept of 0.5 T; median time with
    average altitude = 0.3 T; average time with median altitude = 2.6 T; average time with average
    altitude = 2.4 T so the maximum difference was 2.3 NM.

    Seems accurate enough for me especially for flight navigation where the accepted uncertainty in the observation is 7 NM. (2 sigma)

    gl






    --- On Sat, 5/5/12, Alexandre E Eremenko <eremenko---.edu> wrote:

    From: Alexandre E Eremenko <eremenko---.edu>
    Subject: [NavList] Re: AN5954 bubble octant by Bausch and Lomb
    To: NavList@fer3.com
    Date: Saturday, May 5, 2012, 7:31 AM


    Gary,

    This time it is the right sextant, thanks.
    (I have not figured out yet how can one search and find anything
    in the list files database:-)

    Unfortunately the description is too brief, and some parts of it
    are not clear.
    For example, the sentence that "the interval between two series
    must be approximately 6 seconds".
    During these 6 seconds you are expected to:

    a) read and record the reading, (which involves "rotating the drum until
    the median index is under the index line"),
    b) reset the scales
    c) find the star again, and align it with the bubble

    All these steps they recommend to do in 6 seconds:-)
    Seems unrealistic to me.

    The details are still not clear, but apparently they assume that when
    you shoot VERY quickly (once every 6 seconds), the change of the altitude
    during the time of observation (90 seconds) can be neglected.
    In fact, this change can be as large as 22', but under normal conditions
    (lattitude not too small) it is less.

    Anyway, they are apparently assuming that the effects of acceleration
    of the airplane are larger than the effect from the change of altitude
    in 90 seconds.

    Moreover, they recommend to use the average time of the beginning and the
    end of two observations. For one observation, the time can be 45 sec off the actual moment of the selected shot.

    So it looks like they are aiming at roughly 10'-15' accuracy under the best
    conditions.

    Alex.




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