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I've held off commenting, but I see two problems with this method:

1.  It was suggested that this method could be applied iteratively until
the difference in longitude was small enough that the course segment was
a straight line.   But is this technique any easier or more useful than
applying the standard formula that gives you the latitude of a great
circle for any given longitude (knowing the starting and ending
latitudes and longitudes, of course)?  I would think it would be easier
for a navigator to say "I think I should recalculate course for every X
degrees of longitude traversed"

2.  Any great circle course, when plotted on a Mercator chart, looks a
curve swinging towards the nearest pole and then back down again.  The
rate of change of a course is greatest in the higher latitudes.  If I
were trying to translate a great circle course into steering directions,
  I'd want to calculate course direction more frequently near this
northward (or southward) peak than at lower latitudes.

My bottom line is that this is indeed a neat formula and one that I'm
going to add to my list of formulae associated with great circles, but I
suspect it isn't about to upset more traditional ways of calculating
course segments along a great circle

Lu Abel

Bill wrote:
> George wrote:
>
>
>>I haven't come across that method before. It seems a simple way to
>>split up a long ocean passage. It's exact, not an approximation, and
>>it does seem to give the right amswers. Can anyone see snags?
>
>
> Outstanding George, and simple. Thank you for an excellent contribution.
>
> Snags?  The obvious--cosine or tangent of 90d.  I imagine a bit sketchy in
> areas approaching 90d with a pocket calculator.  I did play with departure
> and destination latitudes approaching zero and those seem to be a wee bit
> off at first blush. I need to compare that to other methods of calculation
> before I can say for sure.   If there is a difference, I don't know how much
> is contributed by the use of a pocket calculator.  At any rate, I don't
> foresee that situation as a problem in the practice of real-world sailcraft
> navigation.
>
> The method seems to accept conventional signing of north and south
> latitudes, and east and west longitudes without so much as a hiccup.
>
> Under the category of "small things amuse small minds" it was so simple I
> could not resist playing with equal departure and destination latitudes 1'
> and 1" north of the equator, with longitude difference approaching 180d.
> Fun and interesting to see at which point it routed me over the pole instead
> of along an equatorial path.
>
> Bill
>
>
> >
>

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