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    Re: Traditional navigation by slide rule
    From: Paul Hirose
    Date: 2016 Oct 25, 09:36 -0700

    On 2016-10-20 12:43, Bob Goethe wrote:
    >
    > Scale ST, which currently deals in values from tangent values from 0.01 to 
    0.1, would - if extended - deal in values of 0.0096 to 0.105.
    > Not as clean for the hypothetical-slide-rule-novice for whom I am trying to 
    design the rule and write the manual.
    
    Did you notice how it's done on the Deci-Lon? The trig scale labels
    ignore the extensions. They show only the nominal scale ranges. E.g.,
    the SRT scale is marked "0.01 to 0.10," though its true range is .00960
    to .1047.
    
    Also, scale extensions need not go out to the next numbered graduation
    as on the Deci-Lon. They could extend only to the next convenient
    graduation. A danger there, however, that the additional graduation
    could be perceived as an index. That won't happen on the Deci-Lon since
    the extensions are so obvious.
    
    
    In the Mark 1 user manual, there's an arithmetic error in Step 3 at the
    top of page 49. The minutes in the result are wrong. However, the next
    line uses the correct value.
    
    There's a mistake or omission in the Bygrave rules, or I'm doing it
    wrong. Please check this southern hemisphere example:
    
    L = S 27, d = S 21, LHA = 79, H = 79
    approx correct az, el = 255, 19
    
    1. W = atan( tan d / cos H ) = 63.6
    
    2. X = (90° - L) ± W
        – if contrary name
        if meridian angle > 90, X = 90° - L - W
        Take absolute value. X = 126.6
    
    3. If X < 90°, then Y = X
        If X > 90°, then Y = 180 - X = 53.4
    
    4. Az = atan(cos W / cos Y * tan H) = 75.4
        Use N if Dest. is N of Your DR
        Use E if Dest. is E of Your DR
        Az = N75.4W = 284.6
    
    5. Hc = atan(cos Az * tan Y) = 18.7
    
    That's the correct altitude, but azimuth is wrong. It should be about
    15° south of west, but my value is north of west by the same angle. What
    do you get?
    
    The Bygrave simulation in my Monte Carlo accuracy measurement software
    works correctly. But its computations are arranged differently from
    yours. For one thing, azimuth angle is always measured from the elevated
    pole (south, if the assumed latitude is south of the equator) and
    increases east or west up to 180°.
    
    http://fer3.com/arc/m2.aspx/Bygrave-formula-accuracy-10-inch-slide-rule-Hirose-jul-2009-g8985
    
    

       
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