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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: slide rule sight reduction accuracy
From: Greg Rudzinski
Date: 2009 Jun 16, 16:02 -0700

```Wow! Great work Paul. Thanks;-)

On Jun 16, 3:35�pm, Paul Hirose  wrote:
> Greg Rudzinski wrote:
> > Would it be possible to simulate for both 10" and 20" slide rules
> > using the altitude sight reduction formula
>
> > ALT = Inverse SIN ( COS meridian angle x COS declination x COS
> > latitude
> > � � � � � � � � � � +/- SIN declination x SIN latitude)
>
> That's about the easiest problem you could have given. In a slide rule
> simulation there's no need to simulate table lookup. And, since the
> sight is worked from the DR position, I don't have to simulate plotting
> a LOP from an assumed position. So I was able to knock this out in one
> sitting.
>
> I consider the basic slide rule operation to be two settings followed by
> one reading. These are assumed to be without error. However, right
> before the reading is taken, I simulate giving the cursor or slide (as
> the case may be) a tiny random nudge equivalent to .1% root mean square
> error in multiplication.
>
> The magnitude of the nudge may be modified to suit the actual formula.
> For instance, the triple cosine product requires three settings and one
> reading. That's four operations vs. the nominal three. Error will
> increase with the square root of the number of operations, so the nudge
> is multiplied by the square root of 4/3.
>
> I assumed a 20 inch slide rule is equivalent to a 10 inch with the nudge
> cut in half.
>
> Addition is assumed to occur without error.
>
> For each test run I used 500,000 randomly generated targets. Observer
> latitude was in the range 0 - 70 degrees. Here are the root mean square
> and worst case errors:
>
> � � � � � � 10 inch � � � �20 inch
> � �alt � � RMS �worst � � RMS �worst
> � 0 - 30 � 1.9' �14' � � �1.0' � 7'
> 30 - 45 � 3.6' �20' � � �1.8' �10'
> 45 - 75 � 8.1' �64' � � �4.0' �34'
>
> � 0 - 75 � 4.7' �63' � � �2.4' �29'
>
> In all test runs, practically 95% of the solutions were accurate within
> twice the RMS figure. The worst case results always occurred near the
> upper altitude limit.
>
> --
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