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    Re: AN5954 bubble octant by Bausch and Lomb
    From: Gary LaPook
    Date: 2012 May 8, 10:11 -0700
    Take another look at what I did. If you are taking multiple readings of the altitude of the horizon with a marine sextant for the purpose of determining index error then you are right, that readings should be constant. I was not doing that, I was measuring the rapidly changing altitude of the sun over a four minute period. My purpose, on that occasion, was to determine the index error but the sun didn't know that, for all it knew I was taking these altitudes for the purpose of finding a small island. My results show what results from taking a series of sights for the purpose of navigation, and averaging them or taking their median.  Note  the conclusion that the possible error from using the median instead of the arithmetic mean for the purpose of navigation is only 2.3 NM, nowhere near the error that you postulated so, that for the purpose of normal navigation, the " median is [ NOT] useless."

    --- On Tue, 5/8/12, 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: Tuesday, May 8, 2012, 5:59 AM

    Gary,
    For checking the index error, median is not worse than average,
    and actually better than the average.
    As for any quantity which does not change quickly.

    Altitude, unlike the index error changes quickly.
    So quickly that the sequence of altitudes you take
    is very likely to be monotone (increasing or decreasing),
    or almost monotone.
    In this case, median is useless.

    The fact that they made this sextant shows that
    they NEGLECT this change of altitude, and treat it
    as a quantity that does not change.
    This means that their accuracy goal was smaller than this change.

    Alex.

    On Tue, 8 May 2012, Gary LaPook wrote:

    >
    > 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. 34? 16.6' N, 118? 54.0' W. Center of the sun.
    >
    >           23:46:00  35? 17'
    >                     14         06
    >                      29       09  
    >                      43       08
    >                     59       06
    >               47:15        02
    >                    28       01
    >                    40  34? 58
    >                    58       52
    >
    >
    >
    > 23:48:18  34? 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 34? 39' while the
    > average altitude was 34? 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 34? 51.5' while the average altitude was 34? 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---purdue.edu> wrote:
    >
    > From: Alexandre E Eremenko <eremenko---purdue.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.
    >
    >
    >
    >
    >
    >
    >
    > Attached File: http://fer3.com/arc/img/119465.average vs. median.pdf
    >
    >
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=119465
    >
    >
    >
       
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