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    Re: The Running Fix on an Ellipsoid
    From: Robin Stuart
    Date: 2017 Feb 6, 09:09 -0800

    It is gratifying to see the interest that this topic has generated. I would like to address Gary’s earlier criticism that was later clarified here. I hope that he will take it in the good natured way in which my comments are intended. I have been searching for some sort of analogy to how I interpreted Gary's words. The best I have come up with is something like “This dishwasher makes lousy toast”. That criticism would only be valid if it had failed in what it set out to do.

    The claim of the paper that is made in the abstract is “A simple rapidly-convergent iterative procedure to obtain a running fix is described that avoids the notion of advanced LoPs and is readily applicable to both the sphere and ellipsoid.” And there’s an implicit claim that it is done right. That’s what is stated, that’s what was delivered, that’s what I stand by and am prepared to take it on the chin for if it’s wrong. Anything else…well…take or leave it.

    There was never any claim made that this would revolutionize celestial navigation which we all understand works just fine up to the level of accuracy required. In fact during the review process I was asked to put a number on the difference between the result in the example and what you get from graphical methods. Here’s my response

    Since navigators have been making use of plotted running fixes in practice for some considerable time it should be expected the deviation from the true position cannot exceed a few tenths of a nautical mile and I have checked that there are no unexpected surprises in the example given in the paper. To eliminate uncertainties introduced by manual operations I performed a calculation that mimics plotting the running fix on a standard plotting sheet centred on 48°N 134° W which is also used as the initial dead reckoning position. This fix differs from the one in the paper by 0.13 nautical miles which is at a level consistent with expectations.

    I am uneasy at quoting a single comparative number because of the many variables upon which plotted fixes depend. These include

    • ·       The actual dead reckoning positions or assumed positions if tables are used
    • ·       Whether the fix was plotted on a plotting sheet or Mercator chart
    • ·       The parallel on which the plotting sheet or chart is centred
    • ·       Whether a correction for the curvature of LoP’s is applied
    • ·       Pencil thickness verses plot scale etc.

    The problem of the running fix on the sphere has received a great deal of prior attention on Navlist (some links are given here) and an incorrect solution was discussed in print by the late George Huxtable. It is not problem that to my knowledge had ever been given a satisfactory solution. There is mention of it for the case of the ellipsoid in Williams, Geometry of Navigation but he doesn’t push it through and suggests going about it in a way that is more complicated than necessary i.e. he treats it as a 2 parameter problem. On that basis I consider it worth taking a look into.

    At the end of the day the key lessons from the paper in my opinion are

    • Trying to generalize the notion of an advanced LoP from the plane to the sphere is unnecessary and unhelpful.
    • The solution can be reduced to one of finding the root of a non-linear equation in just one variable.
    • The solution is simple enough that it can be pushed through for the case of the ellipsoid (which I think is surprising and very cool but you don’t have to agree.)

    Robin Stuart

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