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--- George Huxtable  wrote:
> Jeff Schroeder asked, on 17 Feb.-
>
> >Can someone point me to spherical trig (great circle sailing)
> formulas
> >for determining destination Lat & Lon, if given departure Lat & Lon,
> >true course, and distance travelled?
> >
> >I have made stabs at trying to flip around the cel nav Hc and Zn
> >formulas into what I'm looking for, but must admit the weakness of
> my
> >math skills.  I can't figure out how to get Lat & Lon out of it
> without
> >already knowing one or the other.
>
> =================
>
> Jeff's question is beguilingly simple, but invites some further
> questions.
>
> He specifies great circle sailing, but then specifies "true course".
> And,
> of course, in great circle sailing, there's no "true course"; the
> course
> has to be adjusted all the time to keep to the great circle. What can
> be
> specified is the "initial course" that you start off with. The
> question
> Jeff hasn't asked yet (but will need to ask next), if he actually
> plans to
> steer such a great-circle path, is what adjustments need to be made
> to his
> course as the voyage proceeds.
>
> It would be helpful if Jeff were to explain more clearly what he has
> in mind.
>

George-

How pleased I am that my beguilingly simple question happened to be the
one with which you selected to reawaken the list!

Surely it is beguilingly simple to you and many others, but to me it is
simply beguiling!  As I humbly admitted, I really don't understand
trigonometry.  I understand the theory behind the navigational
triangle, the included sides and angles, and can work the standard
altitude and azimuth formulae by rote with considerable acumen, but can
neither explain their workings nor disassemble and reassemble them to
serve another purpose.  I hope this flaw in my character is not too
unforgivable for this list - I promise I will try to learn plane and
then spherical trigonometry, someday.

My goal was simply to determine a new DR Lat & Lon, given a starting
position, course, and distance traveled, by calculation rather than
plotting, in order to avoid the errors inherent in plotting, e.g.
pencil width, inexact measurement, inexact angle transfer, and my bad
eyes.  I could then plot to the "accurately" calculated point, to avoid
introducing my own plotting errors into example problems.

I suppose I misstated that I wanted a great-circle course.  With the
typical length of a DR leg, and my goal, I don't think the difference
will be significant.  I did assume that calculations based on the
great-circle methods would be more accurate than plane calculations,
and that's why I worded my question that way.  (I'm working on the
scale of a standard Universal Plotting Sheet)

I actually succeeded in using Paul Hirose's suggestion to "rotate" the
triangle, substitute values, and use complements of values (90 - A).
But I failed miserably in trying to simplify the formulae by
substituting the complementary trig functions.  If I knew what I was
doing (or received several more hints) I'd bet there was a much simpler
formula hiding in there somewhere.

Thanks,
-Jeff




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