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Geoffrey & Others, yes the shaded areas of uncertainty can be quite
different from run to run, in size, shape, and orientation.  This is
perhaps better shown in the figure below.  Note how the orientation of
the long axis of these areas follows that of the previous LOP.  The
size can vary because of run length, and unusually variable winds,
drift, heading changes, etc.

The important point is the superior accuracy of the new LOP collapses
this uncertainty to the dark blue line segment along the new LOP.  The
width of this segment is controlled by the LOP's accuracy, and its
length by its extension across the DR uncertainty (the shaded area).

Thus as a long run of fixes evolve, the various orientations of LOPs
will limit the uncertainty in all directions.  However yes indeed, if
the LOPs all have the same direction, the uncertainty along that
direction will continue to grow, but the uncertainty perpendicular to
that LOP direction will maintain the LOP's accuracy.  In practice, we
usually have LOPs varying in direction from observation to
observation.  And the navigator should try to obtain such LOPs,
whenever possible (as with the TRF).

The shaded uncertainties surrounding the DRs are the max extend of
realistic possibilities of DR error.  Thus an EP can not fall outside
of this area unless something is very wrong: that would dictate
checking the LOP, knotmeter, compass, plotting, etc., etc.  Of course
the navigator must use his own judgment on whether the EP is
unrealistically far off.

So it seems that the EP running fix is superior to the traditional
running fix because:
(1) it never gives spurious results for small LOP crossing angles
(2) is always closer to the EP than the TRF
(3) allows for easier and better judgement calls on navigation errors
(4) gives the same result as the TRF for sufficiently small crossing
angles
(5) is easier to plot.

These comparisons with the traditional RFIX arise from the explicit
assumptions it uses: that the estimated track component perpendicular
to LOP1 is accurate and that component of estimated track parallel to
LOP1 is completely useless.  I've yet to hear a justification for
these weird assumptions.

JK

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