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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: Classic Trig Log Sight Reduction Revisited
From: Hanno Ix
Date: 2014 May 29, 21:41 -0700
Greg,

I am astonished you managed to get this on a single index card!

I don't know what your opinion is re: angles in arcmin only. It is strange at first,
of course. But this technique made it possible to compress the cos() table
to just 2 pages. Also, once you are in the arcmin world you need
no more sexagesimal conversions anymore. Besides, the difference Hc - Ho
will be in arcmin - hopefully - anyway.

We have not touched here on the most interesting feature of this method:
A large number of simulations showed that the rounding error is
never larger than +- 0.5 sm no matter the values of D,L, and t!
As we know, this is not the case for Ageton, Dreisonstock and
log - methods in general.

I would be interested to learn about the experiences of others who
try out this method.

Hanno

On Thu, May 29, 2014 at 7:36 PM, Greg Rudzinski wrote:

Nicely done Noell ! Thanks for posting.

Greg Rudzinski

Re: Classic Trig Log Sight Reduction Revisited
From: Noell Wilson
Date: 2014 May 29, 06:51 -0700

This inspired me to finish my "multiple ways to do sight reduction" in Excel. That said, I failed in getting Excel to recognize all the terms and to write everything so each step could be followed. The final result is a mix of Excel, longhand, slide rule, and calculator.

I started this to illustrate how we ended up expressing negative logs as 9.xxx-10 but I ended up not answering that question. Someone smarter than me, and without a calculator, figured that the logCos of 42.175 Deg is -0.13012 and expressed that as 9.869875 -10. It's easy with a calculator but daunting without.

Anyway, the attached is for a different problem, from an Ageton example, with:
Lat 42_10_30
Dec 23_06_24
t 61_33_42 and an answer in Ageton of Hc = 36_01.5 and Az = 90.

In the attached:
First is the input, formula, and answer. Angles as decimal degrees for Slide Rule.
Second is the result with a 10" plastic slide rule similar to a Deitzgen 1733. I was raised with a slide rule and I usually get surprisingly good results if the angles are mid-range.

Third is Cos and Sin as decimals multiplied by calculator with my longhand result in a separate box to the right.

Finally, a calculator used to get logs as negative numbers and making the calculation using those negative numbers. The calculations are repeated to the right in the standard 9.xxx -10 format of the Trig tables.
Regards, Noell
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