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    HO 211 (Ageton) accuracy test
    From: Paul Hirose
    Date: 2009 Jun 24, 19:46 -0700

    I applied my sight reduction simulator to the HO 211 ("Ageton") method.
    Altitude accuracy (square root of the mean squared error) was 1.2
    minutes and azimuth accuracy was 2.7'. About 95% of the altitudes were
    within .8' of the truth. The worst altitude was 29.6' off.
    It's well known that HO 211 becomes increasingly inaccurate in azimuth
    as the body approaches exactly east or west. The worst azimuth error I
    found was 95.7', at (correct) azimuth 271°35.7'. However, errors that
    bad were rare; only .01% of azimuth errors exceeded 1°. The worst errors
    always occurred at high altitudes. If max altitude was restricted to 60°
    (vs. my normal limit of 80°), max azimuth error was 55'.
    The possibility of an occasional poor altitude is not so well known. For
    example, my program flagged this as bad: latitude = +10°39.4', LHA =
    90°39.0', and declination = +40°12.0'. Work it by hand.
           2.8  A(t) (t = 90°39.0')
    + 11702    B(dec) (dec = 40°12.0')
       11704.8  A(R)
       19013    A(dec)
    - 19013    B(R)
           0    A(K) (K = 90°00')
       90 00.0  K
    - 10 39.4  lat
       79 20.6  K - lat
       19013    B(R)
    + 73294    B(K-lat)
       92307    A(h) (h = 6°50.5)
    The correct h is 6°21.8'.
    Note that angle K is somewhat indeterminate because A(K) isn't even
    known to the nearest tenth, and 11 entries in the table (90°00' through
    90°05') have an A value of 0.0.
    I suspect that K very near zero is a warning of poor altitude accuracy,
    though I haven't worked additional problems to confirm it.
    This wasn't as easy as the slide rule simulations. For HO 211 I had to
    simulate a table with entries every .5' and values of A and B rounded to
    the nearest integer, except that small values are rounded to the nearest
    tenth. My simulated navigator always picked the closest table entry but
    did not interpolate.
    The simulated latitudes were from 0 to 70 and altitudes from 5 to 80. As 
    before, the random latitudes and altitudes were weighted so the density 
    of points on the sphere would tend to remain constant instead of 
    increasing near the pole and zenith.
    I configured the program to generate 500,000 problems per run. Why not a
    million? Short attention span. Half a million run fast enough that I can
    stare at the screen waiting for results without becoming impatient.
    I filter out messages with attachments or HTML.
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