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    Re: HO 211 (Ageton) sight reduction accuracy
    From: Paul Hirose
    Date: 2016 Jun 18, 22:39 -0700

    On 2016-06-15 14:53, Robert VanderPol II wrote:
    > You indicate that for 0.5^o tabulation, t<82^o and >98^o and dec less than 
    75o max error is 2.9'.  Should that read t or K?  82^o>K<98^o is what 
    recieves the caution in Ageton, Pepperday and Bayless as I recall.
    It's not clear what you're referring to, especially since some of the
    angle symbols are malformed, but one thing I said was, "if we use the
    standard table, do not interpolate, exclude all sights where t is within
    8° of 90, and all declinations greater than 75°, the max error decreases
    to 2.9'."
    Yes, I did mean t. I realize the danger zone is conventionally defined
    in terms of K. But as I said in a previous message, that's inconvenient
    for the navigator. I'll demonstrate. Suppose t = 83 45.7, dec = 55 07.7,
    lat = 16 07.5. Take the nearest tabular values with no interpolation.
    To attain the error statistic stated above, you'd normally discard the
    sight because t is too close to 90. But let's use K, and interpolate
    B(R) if appropriate.
    1. A(R) = A(t) + B(dec) = 258 + 24279 = 24537
    2. B(R) = 8470
    3. A(K) = A(dec) - B(R) = 8596 - 8470 = 126
    4. K = 85 38, which is in the danger zone, so recalculate starting with
    step 2, and interpolate B(R) from A(R). The relevant part of the table is:
    angle      A     B
    34 38.0  24540  8470
    38 38.5  24531  8475
    2. Since 24537 is 3/9 = .3 of the way from the upper A value to the
    lower, take the corresponding B(R): 8471.5.
    3. A(K) = A(dec) - B(R) = 8596 - 8471.5 = 124.5
    4. K = 85 40.0, which is 2 minutes different from the non-interpolated
    5 K~L = 69 32.5
    6. A(Hc) = B(R) + B(K~L) = 8471.5 + 45663 = 54134.
    7. Hc = 16 42.5. That's only 0.1' less than the correct altitude. The
    good accuracy is probably because t is not very far into the danger zone.
    But note the extra work. You look up B(R), use that to compute A(K),
    look up K, and observe that it's in the danger zone. Therefore, repeat
    the steps, except with an interpolation from A(R) to B(R).
    Time can be saved by using A(K) itself as the criterion: interpolate if
    it's less than, say, 400. It's even simpler to use t instead of K, since
    you know from the beginning whether or not to interpolate.
    If you stipulate declination < 75 (which includes the 57 navigational
    stars), and exclude sights in the danger zone, the error statistics are
    practically the same whether the zone is based on t or K. So why not do
    things the easy way?
    If practical, the safe strategy is to not take sights in the danger
    zone. Interpolation is a hassle, and it's easy to make a mistake since
    the A and B values increase in opposite directions.
    Of course staying out of the danger zone means some extra care planning
    your shots. Still, if you can live with the limitation, an RMS altitude
    error around 0.3' is sufficient for real world navigation. For special
    purposes such as evaluating your sextant technique that's probably not
    good enough, though.

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