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    Re: Rejecting outliers
    From: Gary LaPook
    Date: 2011 Jan 9, 17:33 -0800
    I am attaching clearer copies of the MOO and MOB tables from H.O. 249.

    gl

    --- On Sat, 1/8/11, Gary LaPook <glapook---.net> wrote:

    From: Gary LaPook <glapook---.net>
    Subject: [NavList] Re: Rejecting outliers
    To: NavList@fer3.com
    Date: Saturday, January 8, 2011, 5:48 PM

    Examining the MOB table again reveals that for latitudes of 20° or less the worst case is 0.4' altitude change per minute for a 5° change in latitude; 45° or less, 0.9' and for 60° or less, 1.1' for a 5° change in latitude. It is hard to believe your DR latitude would ever be off by 5°, 300 nm.

    As to change of rate due to change in azimuth, it changes in the opposite sense with latitude, becoming smaller with increases in latitude. Worst case at 20° or less latitude is 0.5' for a 2° change in azimuth; 45° latitude, 0.4'; 60° latitude, 0.3' per 2° change in azimuth. At 60° latitude the azimuth will change 2° in 4 minutes for declinations of 29° or less and 3° for declinations up to 45° (there are only 10 listed stars with declinations greater that 29° north) so even at that latitude, a 30 nm error in longitude would result in less than a 2' difference (for most stars) in the altitude computed with the MOB table (resulting in a 2' error in the graph of the slope) in a four minute period so this method should be usable even at high latitudes.

    As for difficulty in actually measuring the azimuth, if you pre-compute the data for presetting the sextant then you will have the azimuth to use in computing the slope with the MOB and MOO tables.

    gl

    --- On Sat, 1/8/11, George Huxtable <george{at}hux.me.uk> wrote:

    From: George Huxtable <george{at}hux.me.uk>
    Subject: [NavList] Re: Rejecting outliers
    To: NavList@fer3.com
    Date: Saturday, January 8, 2011, 1:57 PM

    Gary wrote-


    "But for calculating the slope the DR doesn't need to be particularly
    accurate as the slope is determined only by your latitude and the azimuth
    of the body, which you can measure to sufficient accuracy. If you scan the
    Motion Of the Body table from H.O. 249 at:

    http://www.fer3.com/arc/img/102321.mob%201.pdf

    you will see that the rate of change in altitude is very insensitve to
    errors in latitude and azimuth. For example, looking at the MOB table for
    my data where my DR latitude was 14° 25' and the azimuth was 103° true, the
    tabulated values for the change in altitude for one minute of time changed
    only 0.1' for a 2 degree azimuth change and by only 0.2' for a 5 degree
    change in latitude. So for a five minute observation period, if my DR
    latitude had been wrong by five degrees the slope would be off by only one
    minute of altitude. Similarily, the measured azimuth would have had to have
    been off by four degrees to produce a one minute error in the slope.
    Scanning H.O. 249, volume 2 shows that to produce an error of four degrees
    in the azimuth my DR longitude would have had to have been off by ten
    degrees, 600 nm!"

    =============

    Gary's conclusion is right, though his example was not a typical one.
    Observing from within the tropics a body that's nearly due East, that body
    will be climbing more-or-less vertically , and so its rate-of-change of
    altitude will be near the maximum possible, of 15º per hour, and will
    therefore be very insensitive to changing the parameters.

    But it's not the same the whole World over. From higher latitudes, when
    observing bodies that are climbing diagonally across the sky, the
    rate-of-change of altitude will be less, and it will have a greater
    dependence on latitude and azimuth.

    Even so, it will often allow the rate of change to be calculated more
    precisely than it can be measured, depending on the precision of the
    observation and the accuracy with which the position is known.

    George.

    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.





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