NavList:

   

Reply

I was 13 years old 48 years ago but have always been intrigued with the
mysteries of celestial navigation.  So I finally got on the web and
searched for some pertinent links (including this list).  Surprise, it's
very simple in concept.  A fix is obtained from the intersection of the
circles of equal altitude obtained from sextant sightings to several
heavenly bodies.

Well it seems no one really does it that way because of plotting scale
problems.  The solution requires a sight reduction procedure that
refines a dead reckoning position.  OK, I can't argue against that time
proven methodology.  With a computer, what's wrong with a direct
calculation in the event that you don't have the 'foggiest' idea of
where you are?

Getting back to the intersection of circles of equal altitude, I had to
convince myself of the validity of this concept with real world data.
How accurate can a 'low tech' approach be?  Looking at the Dec and GHA
table values to 0.1 minute precision (about 600 Ft) suggests nautical
mile accuracy is possible if the sight timing and measuring process is
under control.  That's not too bad.

I found some useful equations for spherical earth calculations (Aviation
Formulary by Ed Williams) and wrote a software program that calculates
the locus of Lat-Lon points at 0.01 degree increments around the
Geographical Position of a body.  I borrowed a plastic Davis sextant and
took it on vacation to Myrtle Beach, SC.  On a clear morning, I trekked
to the beach, checked sextant alignment per its instructions, measured a
reference position with time by GPS and finally, took several sun sights
timing them with an alarm chime from my watch.

To my amazement, a point on a resulting equal altitude circle passes
within 0.8 nm of the GPS position!  Close enough?

Obviously, the next step would be to rewrite the software to accept data
from additional sightings and calculate the circle intersections.
That's easier said than done.  Many hours of web searching have failed
to reveal any equations to do this.  I can't believe that during several
thousand years of spherical geometry study, someone has not solved this
problem.  It might be a horrendous problem but the solution is out there
somewhere.  GPS is based on a similar concept.

I'm not a mathematician and will not attempt to derive the equations.
I'll look into solving this problem numerically.  But, that is a brute
force approach that is not particularly satisfying from an aesthetic
viewpoint.


                                               ---  CHAS

   

Reply