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Lu:

I have an old DOS navigation program which I love, and which has four options 
for Great Circle calculations plus one for rhumb line:

Planning by Great Circle/Mercator Sailing

 A  GREAT CIRCLE
 B  GREAT CIRCLE with LON INTERCEPT
 C  GREAT CIRCLE with INCREMENTAL DIST
 D  COMPOSITE SAIL with MAX LATITUDE
 E  RHUMB LINE

It's called PC Navigator and has been around for years.  I love it's 
simplicity, accuracy, and incredible speed.  Option "B" will give you a 
listing of the LAT/LON at intervals you determine (e.g., every 5 degrees of 
longitude) and the course, distance, and total distance.

It also does other calculations, e.g.,

Piloting and Dead Reckoning

   F  COURSE & SPEED MADE GOOD
   G  COURSE & SPEED STEERED
   H  TRUE WIND
   I  APPARENT WIND
   J  DISTANCE TO OBJECT
   K  DEAD RECKONING
   L  UPDATE DR

        and

Positioning by Celestial Observation

   M  DAWN PLANNER
   N  NOON PLANNER
   O  DUSK PLANNER
   P  BODY FINDER
   Q  RISE, TRANSIT & SET TIMES
   R  ALMANAC
   S  SIGHT REDUCTION to LOP
   T  NOON FIX
   U  LOPs to FIX
   V  DELETE LOP from FILE

File Management Utilities

   W  EDIT DATA FILE
   X  SET DATE & TIME

Bill


At 11:33 AM 7/25/99 -0700, you wrote:
>A friend of mine who is not a sailor but an avid electronic gadgeteer
>showed up the other day with his new handheld GPS.  He asked me how far
>away the destination point could be in finding course and distance. "As
>far as you want."  To demonstrate, I pulled out an atlas and we punched in
>the L/Lo of Times Square in New York City (we're in San Jose, California).
>
>He noticed the indicated course was a bit more northerly than one would get
>from the atlas.  I told him the GPS was calculating great circle courses,
>which always run more pole-ward than straight-line (rhumb line) courses.
>He's a smart guy -- he's heard of great circle courses and understands what
>they are.
>
>He asked how to calculate a great circle course.  I pulled out the USPS JN
>text and looked up the spherical trig formulae.  He whipped out his laptop
>computer and in a couple of minutes had an Excel spreadsheet which took two
>L/Lo's and calculated distance and initial heading.  The results were in
>excellent agreement with what the GPS was displaying for course and
>distance to NYC.
>
>A couple of days later he asked: "Lu, how do you steer a great circle
>course?  How do you know what your headings should be as you sail or fly
>along a great circle?"
>
>I told him that one would plot several intermediate points of the course on
>a Mercator chart and then steer the rhumb-line courses between them. Then
>I realized I didn't know how to find intermediate points.
>
>My copy of Bowditch has grown feet and disappeared.  Dutton's only advice
>(as well as the USPS's) is "use a great circle chart and transfer points to
>your Mercator chart."
>
>Since a great circle course is one side of a spherical triangle with the
>start and end points and the elevated pole as vertices, I would assume I
>could calculate the latitude of a point on the course for any DLo, but my
>spherical trig is really rusty and I don't have a book of formulae.
>
>I'll also point out that one could solve the problem in a fraction of a
>second on a computer using a technique known as iteration:  If I want the
>latitude of a point on the course for some intermediate longitude, guess
>one (say by simple plane trig using the initial course), calculate the
>course to it from the starting point, if the course is more pole-ward than
>the great circle then the assumed point's latitude is too great and it
>needs to be reduced; if the course is more equator-ward, then the latitude
>is too low.  The key is to adjust the latitude by an amount which is
>proportionate to the course error.  If one does this repeatedly, the
>assumed point will get as close as one wants to the great circle.
>
>Thanks for helping fill out what I suddenly realize is a hole in my knowledge!
>
>Lu Abel
>

   

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