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    Re: St Hilaire not Iterative was: Finding The Symmedian
    From: George Huxtable
    Date: 2010 Dec 30, 00:07 -0000

    On 25 Dec, Andrew Nikitin explained why he though it would be unproductive 
    for a navigator using graphical techiques to reiterate a fix of LOPs, as 
    follows-
    
    "A navigator using plotting techniques introduces greater errors
    which stem from these techniques (placing a ruler, drawing line along its
    edge are not exact operations, especially on a small cluttered badly lit
    table which rocks back and forth). Assuming your AP is within a degree,
    the error introduced by Hilaire method would be smaller then the errors
    introduced by the act of plotting lines. Doing second iteration would be
    a waste of time."
    
    ===================
    
    That is a fair comment, but it needs a bit of qualifying. It depends. It 
    depends on the altitude, the geometrical errors getting worse at high 
    altitides. It depend on angle-of-cut between the azimuths of observed 
    bodies. It depends on the accuracy of the Assumed Position, on which Andrew 
    sets an upper limit of 1 degree, but that in turn depends on how good is 
    the dead-reckoning. In the heyday of celestial navigation, how good was the 
    DR of a sailing vessel which had spent a week battling adverse weather, 
    without a sight of the Sun or anything else? Such conditions were not 
    unusual, especially in the Atlantic, in Winter.
    
    I attach Table 4 from vol.2 of my 1981 Bowditch. This is a table of 
    offsets, showing how to bend a straight-line approximation to an LOP, to 
    make it sufficiently curvaceous to be an accurate position line. It also 
    shows the error that remains if, as usually happens, no such adjustment is 
    made.
    
    The maximum such discrepancy in AP that the table contemplates is 45', and 
    because the resulting errors go as the square of that , then Andrew's 
    assumption, that the AP was within a degree, could result in errors that 
    are nearly double those in the 45' column. Those errors can then be 
    considerably greater than a competent plotter  would accept on a 
    plotting-sheet.
    
    The careful navigator can disregard the need for reiterating if his 
    altitudes are all low ones (less than 60º, say), at a good angle of cut, 
    and his Assumed Positions are known to be close to the truth. Or if he uses 
    table 4 to bend his position lines suitably. Or if, being in mid-ocean, he 
    doesn't really care about his position being a few miles out. But 
    otherwise, reiteration may need to be considered seriously.
    
    George.
    
    contact George Huxtable, at  george@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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