# NavList:

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

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Re: Using a slide rule for celnav
From: Hewitt Schlereth
Date: 2014 Jan 20, 18:49 -0800
Gary is absolutely correct about this. Greg Rudzinski and I have several times done reductions on K&E 10-inchers on this site using the fundamental sin/cos formulas for Hc and Z. During WW II, flight navigators used them (rules and formulas). Gary's flat Bygrave takes advantage of tangent functions, is slick and fast. I like the sin/cos way mainly because I long ago memorized the two (very short) formulas.

As Gary points out, I think it's helpful to keep in mind that celestial is a sea of approximations in which decimal points simply drown. "Those damned dots," as Winston Churchill famously said.  :-)

Hewitt

On Jan 20, 2014, at 5:08 PM, "Gary LaPook" <garylapook@pacbell.net> wrote:

A thorough study of thousands of sextant observations taken by professional navigators showed a standard deviation of about 1.5 minutes and if you are using H.O. 229 it states that the accuracy is usually within 0.2' with some weird cases producing errors up to 3.9' in the Hc so don't get too upset about the possible inaccuracy introduced by using the Bygrave formulas on a ten inch slide rule. It's nice to work to a precision of 0.1' in our tables and calculators but we are really going beyond our data if we think that we are going to get a significantly more accurate fix by doing so. This precision is swamped out by the measurement uncertainty, the uncertainty in the Nautical Almanac and in the computations themselves, why only work to a precision of 0.1' why not 0.0001'?

gl

From: Gary LaPook <garylapook---.net>
To: garylapook---.net
Sent: Monday, January 20, 2014 4:33 PM
Subject: [NavList] Re: Using a slide rule for celnav

You're right, he Bygrave does about 1 or 2 minutes of accuracy, about like HO 249. If you want greater precision than that then you must stick to the methods that you currently are using. I hope there is no EMP in your neighborhood.

gl

From: Greg Licfi <cfi{at}licfi.com>
To: garylapook---.net
Sent: Monday, January 20, 2014 9:33 AM
Subject: [NavList] Re: Using a slide rule for celnav

Hi Gary,
Perhaps I'm just misinformed; and in this case I would love to be - so please take no offense if I am.
I think I read somewhere that a Bygrave sliderule can only resolve 1 arc minute(?).
This might be better suited to a aircraft with a bubble sextant (+/- 2 arc minutes after averaging ?) then a ship.
I currently do my calculations with: H.O.229, a smart phone app, ICE, and a scientific calculator.
all of which seem to agree within +/- 0.1 arc minute with the USNO. If it (the Bygrave sliderule) can resolve
better than that I would be a convert for sure. Also; how much resolution do you need on the sliderule?
Back in my college days 3 or 4 decimal places was considered good with a 'K&E Decalon(?)5'
BTW: I'm a big fan of ICE - I run it on my laptop & smart phone with something called 'dosbox' My smartphone
app uses USNO software and data, ICE was a USNO product, as is H.O.229. so you would expect them to all
yield the same results (no?)
~Greg

This new ship here is fitted according to the reported increase of knowledge among mankind. Namely,
she is cumbered end to end, with bells and trumpets and clock and wires, it has been told to me, can call
voices out of the air of the waters to con the ship while her crew sleep. But sleep Thou lightly. It has not
yet been told to me that the Sea has ceased to be the Sea.
—Rudyard Kipling

On 01/20/2014 04:28 AM, Gary LaPook wrote:

But if you are thinking of doing celestial computations on a normal sliderule you should consider using the Bygrave formulas instead of the normal cosine formula because they give greater accuracy. See:

http://fer3.com/arc/m2.aspx/Bygrave-formula-accuracy-10-inch-slide-rule-Hirose-jul-2009-g8985

http://fer3.com/arc/m2.aspx/Bygrave-formula-accuracy-10-inch-slide-rule-LaPook-jul-2009-g9019

Or, you can make your very own Bygrave sliderule which provides even greater accuracy, complete plans are available here:

gl

From: David Cortes <dcortes{at}rwlw.com>
To: garylapook---.net
Sent: Sunday, January 19, 2014 10:48 PM
Subject: [NavList] Using a slide rule for celnav

```To Navlist:

I learned how to use a slide rule back in high school, and it's been 45-plus years.  Can some of you old-timers tell whether it's possible to multiply sin by sin or cos by cos, etc.  n one continuous operation, without putting the rule down to write down the number of the first calculated sin or cosin, etc.?

David

-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Frank Reed
Sent: Monday, January 20, 2014 12:13 AM
To: dcortes{at}rwlw.com
Subject: [NavList] Re: What is a "Class A" sextant?

My understanding of the Kew "Class A" rating was that it was an overall rating. It was the certification required for sextants given to Royal Navy cadets. It combined several factors, and the instrument had to meet various standards on several tests.

You may remember a NavList discussion a few years back about tables of "star distances" published in about 1905 for use with Lord Ellenborough's method of testing sextant arc error at sea (*). In the introduction, the authors say that a "Class A" certification implies among "other things" that the centering error (or "arc error" as we would call it today) amounted to less than 1' of arc maximum. Classes B and C would presumably permit progressively greater arc error, and this same source says that the sextant would be "rejected" (in other words, worse than class C) if the arc error was greater than 3'.

*that discussion was in March 2010, and here's my first message on thee subject, specifically addressed to you personally, in fact. :)

-FER

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