NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Fw: Sight Reduction by Hand you might like
From: Hanno Ix
Date: 2013 Aug 13, 16:15 -0700
From: Hanno Ix
Date: 2013 Aug 13, 16:15 -0700
Well, here it is:
This now is my story on Sight Reduction by Hand - the "prosthphaeresis" - we discussed some time ago. All the
material is in the attatchment. It includes a narrative that starts like this:
I
found myself challenged to be able to do CelNav arithmetic by hand
just as Capt J Cook did, at least occasionally. I started out looking
for the most simple arithmetic method for evaluating hc by hand and
went through my books some time ago, In some Russian math
compendium, translated to English, I found a trig formula I'd never
seen before ( ISBN 978-3-540-72121-5 / pg 81 / equ 2.128). It has
features that are rather unusual but desirable for the navigator. Look
at this:
We are of course used to
sin(hc)
= sin(D)*cos(L) + cos(D)*sin(L)*cos(t).
The book shows that this
expression can be transformed, after some algebra, into:
sin(hc)
= [ cos(D-L) – cos(D+L)] / 2 + [cos(S-2D)
+ cos(S-2L) + cos(S-2t) + cos(S)] / 4
with
the definition S = D + L+ t.
etc.
It turns out to be an interesting subject, and I hope to get some responses from the list members.
Enjoy!
h
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