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John,

>> This is an old topic, but I guess it's time to address it again. <<

Please, no! Asolutely not. Frank Reed has shown you in his message g11185 where you are wrong and even included a beautiful drawing. You have a tendency to redefine time-tested problems, terminology and meanings and then tell us how wrong the old concepts are or how badly we misunderstand them, when in fact only your idiosyncratic interpretations suffer from the difficulties that you bemoan.

The classical running fix is a simple geometrical problem: Given are to lines a and b (the 2 LOPs) and an arrow vector representing the run of the vessel between observations. The task is to place the vector in such manner that its tail coincides with a and the head with b. Unless a and b are parallel to each other, there is exactly one solution. This, and nothing else is the problem of the classical running fix.

Since the problem is not overdetermined, you cannot possibly assume or find an error in the DR track. And since there is no error, the advanced LOP cannot have anything to do with it. You are seeing a problem  where there is none.

There is no such thing as a nonsensical geometrical problem. So, the "Nonsensical Running Fix" must be nonsensical.

Herbert Prinz