Great circle sailing and rhumb line - how to calculate distance and course (bearing) between two points - marine great circle formulas - navigation calculator

Formulas, programs and calculations to obtain distance and course (bearing) between two points - loxodromic (rhumb line) distance and orthodromy (great circle sailing) waypoints - orthodromic and loxodromic navigation - two spreadsheet excel files - (free download and use!)

distance and true course (bearing) between Buenos Aires and Gibraltar .........
great circle sailing (orthodromy) or rhumb line (loxodromic route) ?

You can download and use these files ( they are free ! )

1st file - Great Circle Sailing - Rhumb Line

This simple file provides the following information (navigation data) : course, distances in nautical miles (great circle and rhumb line), initial course and vertex latitude

type	excel file (spreadsheet) -
size	49 Kb
download

a view of the spreadsheet (excel file) :

Coordinates must be entered : latitudes and longitudes (degrees- minutes-seconds) "n" for north latitude, "s" for south latitude, "w" for west longitude, "e" for east longitude

2nd file - Great Circle Sailing - Rhumb Line - Waypoints ( full track ) - Route Graph

A full program for all users (students, sailors, officers and masters of the "merchant navy " .... ) : courses, distances (rhumb line & great circle sailing), orthodromic data ( vertex coordinates ), E.T.A. (estimated time of arrival), compass direction, manual-automatic waypoints calculator and planning routes.

This file is created thanks to the remarkable ability of Jelle Schaap in the development of excel programs. It is a logical evolution and completion of the first file. This feature distinguishes the file from many others currently on the web. The program allows the user to customize all navigation data; 60 waypoints (great circle navigation) and 60 rhumb lines can be managed. Instructions are included in the file.

The sheet "Chart1" shows a diagram with the location of some parameters: great circle navigation, rhumb lines, courses, waypoints ....

This file was created with Office 2007 in a "binary" format so the program can only be used on personal computers with Office 2007 (or later) installed. The spread of Office 97 and Office 2003 is still considerable. It was decided to prepare a compatible version (albeit with limited functions) : a slightly different version of conditional formatting from the "Office 2007 version". In all versions is essential to enable macros before using the program (calculations are not performed without activating the macro, however, see the instructions in the file). Files include translations in languages (English, German, Dutch, Spanish and Italian).

version		size	type
Microsoft Office 97-2003	download	436 kb	.xls
Microsoft Office 2007	download	231 kb	.xlsb

Formulae
calculation for incr. latitude	formula : ( 7915,7 * log tan (45° + lat/2)) - (3437,7 * ee sine lat)
calculation for true course (t.c.) - (bearing) rhumb line	formula : tang. t.c. = longitude difference/increased latidude difference
calculation for loxodromic distance (rhumb line)	t.c. < 45° = latititude diff. * sec t.c. 45° < t.c. < 87° = latititude diff. * tg t.c. * cosec t.c. t.c. > 87° = longitude diff. * cos med.lat. * cosec t.c. excel will use the best formula according to the value of the course (0°-90°)
calculation for orthodromic distance (gc great circle)	formula : cos gc = (sine lat a * sine lat b) + (cos lat a * cos lat b * cos longitude diff.)
calculation for init. course (oc great circle)	formula : ctg oc * sec lat.a = cosec long.diff. * tan lat.b - cot long.diff. * tan lat.a
calculation for vertex latitude	formula : cos hl = cos lat a * sine oc

I'll be happy to receive observations or simple greetings

The author wishes to express his gratitude to Mr. Jelle Schaap for the realization of the file no.2 ( authorization to freely distribute the file included )