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    Re: Single LOP is enough?
    From: Robert VanderPol II
    Date: 2020 Sep 15, 21:37 -0700

    Gary:

    Is there another larger earth involved here? The circumfernece of this earth is 21,639nm so that is the circumerence of the largest circle that can be drawn on it.  And 1° azimuth change would involve moving 60.1nm along that circumference.  Or am I missing something really big (pun half intended)?.

    Letcher's book is my access to HO-208.  His instructions indicate that Lat and t should be whole degrees which means that AP is used for the reduction rather than DR/EP.  Are there different instructions with the original using DR/EP rather than the reproduction I have?

    John Deen:

    If you wanted to plot a line of position for the body shot you would need to measure the azimuth (aim the whole boat at the body), apply corrections for variation and deviation.

    To plot you would need a very large map to plot on in order for your pencil width to not be 100nm wide.

    Mark the GP of the body on the map.

    Now comes the tricky party, the line you want to draw is the great circle direction from your location, not the rhumb line.  On a mercator projection the rhumbline can be drawn as a straight line, but the great circle LoP is a curve who's shape depends on the latitude of you and the body and the LHA and probably something I'm not thinking of just now. It might be possible to use a gnomic projection, but I haven't played with those much so couldn't say for sure.

    I recall reading somewhere that it is posible to plot a very high altitude as an actual circle on a reasonably scale map.  The altitude of the body needs to be up 85° or so.  If you are able to shoot a body that high accurately, then I can think of several ways to measure azimuth to within a couple degrees.  Then you could plot from a single sight, and the azimuth measurement. However shooting that high is extremely difficult.

    Regards,

    Bob II

    Re: Single LOP is enough?
    From: Gary LaPook
    Date: 2020 Sep 15, 11:29 -0700

    For a low altitude observation ~ 0° the radius of the circle is 5,400 nm. The circumfrence is 33,929 nm so one degree along that circumfrence 94 nm. From where would you plot that azimuth? You can't do it from your AP but must do it from the GP. The scale errors would not allow much accuracy. However, you can establish an "Estimated Position" or MPP, Most Probable Position, by dropping a perpendicular from the DR to the LOP. However this is NOT a fix since any error or uncertainty in the DR is carried forward onto the MPP. If you use your DR as your AP (Bygrave slide rule, HO 211, HO 208, etc. but not HO 249 or HO 229) then the intersection of the azimuth line with the LOP is automatically your MPP. In flight navigation it is standard to allow for a DR error of 10% of the distance flown but I have never seen a similar estimate for DR uncertainty in marine navigation.  But using this estimate, then after a day of sailing without a fix the uncertainty circle would be about 12 NM radius so you can mark out along the LOP that estimate both to the right and left of the MPP and you are unlikly to be further out along the LOP. And you should remember that the LOP is thick, about 1.5 nm on each side of the plotted line to allow for commonly accepted accuracy in celestial observations. 

       
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