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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.
    >
    > --
    > I filter out messages with attachments or HTML.
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