# NavList:

## 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: Paul Hirose
Date: 2009 Jun 16, 15:35 -0700

```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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