# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: The Great Circle Challenge
From: Gary LaPook
Date: 2014 Dec 26, 11:35 -0800
﻿Many years ago, in the 1980's, I programmed a small handheld computer, a Casio PB-1000, to do
in flight celestial navigation. It has a total memory of about 6,000 bytes. To make the programs
fit you have to use assembly language for the programs. I have no idea how these programs work
now and it would take me a long time going over the program printout and the manuals for the
computer to figure it out. One of the things I programmed it to do was to calculate great circle
routes. Since you have to make position reports crossing every five degrees of longitude, I also
programmed it to calculate the intermediate points and the rhumb line courses between those points
and the total distance using these RL between points.

So, inputting your data it took one minute and 35 seconds to give the course as 26.3 degrees and
the distance is 4,078.9 NM. It also gives the vertex of the GC as 70̊ 35.2' south, 102̊ 10.1' east
which has no importance for the journey between New Zealand and Hawaii. The RL course 21.1
and the RL distance is 4080.9 NM, only 2.0 NM longer than the great circle showing that
flying a GC in low latitudes offers little advantage over the simpler RL.

LON            LAT               Dist                CR           Cum
Leg 1      175 E          39̊ 56.8' S       103.7 NM       26.3̊        103.7 NM
Leg 2      180             30̊ 52.9' S       596.1               24.2        699.8
Leg 3      175 W       19̊ 29.8' S        734.9               21.6        1434.7
Leg 4      170 W         6̊ 07.6' S         853.6              20.0      2288.3
Leg 5      165 W        7̊ 58.8 N          897.8              19.5      3186.1
Leg 6      160 W      21̊08.4 N          840.9               20.1     4027.0
Leg 7      159̊ 40'W  21̊ 57.0' N          52.1             20.9      4079.1

So, flying rumb line segments to approximate the great circle is only 0.2 NM longer than if flying
a perfect great circle. And notice the characteristic “S” shape to the courses for GC’s crossing the
equator.

Gl

To: garylapook@pacbell.net
Sent: Friday, December 26, 2014 8:21 AM
Subject: [NavList] The Great Circle Challenge

The Great Circle Challenge

Clearly, from recent posts, we all have a favoured way of solving great circle sailings (which we’ll probably never use for real).  Let’s put them to the test by trying something a bit more complicated like a southern to northern hemisphere crossing combined with a crossing of 180degrees E/W.  How about emulating Captain Cook by travelling from Cook Strait (CS), New Zealand to Waimea Bay (WB), Kauai, Hawaii?  Cook followed the pretty route, but we’ll go direct by great circle.  The coordinates are CS 41d 30’S, 174d30’E to WB 21d57’N, 159d 40’W.  Use your favourite method and report back on your answer, the time it took you, and any difficulties encountered.

I’ll stick with the diagram method, because at least I’ll know what I’m trying to prove, and I won’t have as many rules to remember and apply which might or might not work.  Dave

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