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    Re: slide rule sight reduction accuracy
    From: Gary LaPook
    Date: 2009 Jun 16, 17:09 -0700

    Here or my some of my prior posts on the Bygrave.
    glapook---.net wrote:
    > Very interesting.
    > I have recently done a number of trial computations on my 10 inch
    > rules using the Bygrave formulas instead of the sine-cosine formulas
    > and it appears that I get better accuracy. Can you run a simulation
    > similar to the one you did for Greg using the Bygrave method to
    > confirm that this a preferable method if using a normal slide rule for
    > celnav computations?
    > Could you do the same with a Bygrave such as my flat implementation?
    > On my flat Bygrave the Cosine scale from 0 to 89�16' covers 19 cycles
    > each 126 mm long, a total length of 2.394 meters or about 94 inches
    > and the cotan scale from 54' to 89�16' covers 37 cycles for a total
    > length of 4.662 meters or about 183 inches. The original Bygrave is a
    > bit larger but I am curious about the accuracy of the one I developed.
    > I have found that the results fall within 2' and usually within 1' and
    > often right on the money.
    > gl
    > 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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