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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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