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    Re: Sight Reduction Formula Question
    From: Peter Fogg
    Date: 2005 Jan 10, 16:26 +1100

    George Huxtable wrote-
    "Now consider the other formula, deriving Z from its sine. If, in this case,
    that formula has given us sin Z = +0.98, what do we do then? Well, one
    solution is that Z = 88.5 deg, which might well be the right answer. On the
    other hand, sin 101.5 deg is also +0.98, so that's an equally valid answer.
    It could be either, then. How do we discover which is the one we want? In
    this case, there's no simple way, that I know of, to resolve the ambiguity
    by using inspection and logic to determine whether the wanted result is just
    North of East or just South of East."
            I guess simplicity lies in the eye of the beholder. There is a way
    to resolve the ambiguity. Since the virtue of the method is itself
    simplicity, this complication tends to detract from the appeal of the
    method, in the limited cases when it occurs.
    "You will find the advice, in some textbooks, "just take a compass bearing
    on the body, and it should be easy to distinguish which one is right".
    Well, perhaps that's reasonable, in that widely-spread example, but say the
    two possible angles were closer, say 88 deg and 92 deg. Would you be sure
    which was the right one then? And anyway, if you're prepared to accept a
    compass-bearing for azimuth, why are you bothering to calculate it?"
            Because each method acts as a check on the other - either
    reinforcing the same message or raising doubt. Its such an ingrained
    on-board habit, to have back up options for fail safe procedures for
    pretty-well everything. It tends to permeate all aspects of sailing - for
    example, each time the same mooring is picked up, nearly always a banal
    operation, its just as well to have a Plan D and then a Plan E if possible.
            The French version of 'to sail a sailing-boat' is 'naviguer un
    voilier'. In this sense 'la navigation' is what English speakers know as
    'seamanship' - our more narrow sense of navigation is understood as being an
    integral part.
    "No, deriving azimuth from its sine is the worst possible option."
            Not if its virtues outweigh its shortcomings in the vast majority of
     "There's a third option, that for some reason doesn't find its way into
    many textbooks. Get the azimuth from its tan! This formula is- Tan Z = sin
    (hour-angle) / (cos (hour-angle) sin lat - cos lat tan dec) and the rules
    for putting Z into the right quadrant, 0 to 360, clockwise fron North, are-
    If tan Z was negative, add 180 deg to Z.
    If hour-angle was less than 180 deg, add another 180 deg to Z."
            Sounds great. When can we expect to see a production model? Could
    this method be turned into a simple 'look up' table?

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