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## 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, 17:51 -0800
OOPS!
There is the old saying, "to err is human but to really screw up you need a computer"

I input the wrong starting position into my PB-1000 so the answers came out wrong. Please disregard my prior post, here is the correct answers. (I assume that the given coordinates in the challenge were exact and not limited to a one nautical mile accuracy.)

﻿Many years ago, in the 1980's, I programed 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 programed it to do was to calculate great circle
routes. Since you have to make position reports crossing every five degrees of longitude, I also
programed it to calculate the intermediate points and the rhumb line courses between those points
and the total distance using these RL between points.

So, inputing your data it took one minute and 35 seconds to give the course as 25.9 degrees and
the distance is 4,069.1 NM. It also gives the vertex of the GC as 70̊ 55.2' south, 102̊ 19.2' east
which has no importance for the journey between New Zealand and Hawaii. The RL course 20.7
and the RL distance is 4071.0 NM, only 1.9 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          40̊ 43.1' S       52.1 NM          25.7̊           52.1 NM
Leg 2      180             31̊ 40.1' S       594.3               24.0         646.4
Leg 3      175 W       20̊ 13.3' S        737.7               21.4       1384.1
Leg 4      170 W         6̊ 40.5' S         863.3              19.7       2247.3
Leg 5      165 W        7̊ 41.9' N          912.8              19.1       3160.2
Leg 6      160 W       21̊07.4 N          856.1               19.8       4016.3
Leg 7      159̊ 40'W  21̊ 57.0' N          52.9                20.6      4069.2

So, flying rumb line segments to approximate the great circle is only 0.1 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

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