NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: St Hilaire not Iterative was: Finding The Symmedian
From: George Huxtable
Date: 2010 Dec 30, 00:07 -0000
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.