NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: On LOPs
From: Jared Sherman
Date: 2002 Apr 15, 20:36 -0400
From: Jared Sherman
Date: 2002 Apr 15, 20:36 -0400
So far I haven't seen any justification for the "most probable" position, much less for the use of an ellipse (which has 2 focii) rather than a circle (with one focii, i.e. center) when using 3 or more LOPs (which would indicate a need for 3 or more "focii"). Forgive me if the plural of focus is not focii, my latin isn't rusty, it simply "isn't". A valid "most probable position" would have to take into account the individual variations and probable errors inherent in EACH of the LOPs. Graphically this could mean using a thicker pencil to draw each, i.e. if the accuracy of the sextant is 0.2 minutes and the accuracy of the eye on the horizon sight is another .2 minutes, draw the line to reflect the possible range of positions that are derived from being off .4 minutes to each side of the reading. Once each line is drawn, the "most probable" position them becomes that area included under all three zones (the lines plus the extra width around them) and if all three zone do not contain a common area, it would still be most probable that the error in each site be expanded until the zones overlapped. At that point a circle (yes circle) or error could be expanded out to contain the probable positions, or an irregular complex shape that would be possibly more accurate than the circle. I'd be able to do this graphically, but not statistically. I suspect the math would rapidly get more complex than the "use a thicker pencil and make a circle of error" approach, without giving much more useful information.