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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
cases.

 "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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