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    Re: H.O. 249: rounding Ho
    From: Paul Hirose
    Date: 2020 Mar 20, 11:43 -0700

    On 2020-03-18 7:02, Gary LaPook wrote:
    > Your final result is only as accurate as your least accurate input. Since HO 
    249 only provides data to the integer minute it make no sense to combine it 
    with the more precise HO to a tenth of a minute. Just round the HO to the 
    nearest minute, combine with HC and plot the intercept to the whole nautical 
    mile (minute of arc.) If you want more precision in your celnav then you need 
    a more precise method of sight reduction, HO 229; HO 214; HO 208; HO 211; or 
    various computer apps.
    
    I have a somewhat different attitude. The error of the final result is
    the sum (not a simple arithmetical sum, however) of a multitude of
    errors. These include uncertainties in dip and refraction, instrument
    error, assumptions in the assumed position intercept method, rounding
    error in the reduction table, and rounding error in the computations.
    
    That last is under your control, and can be reduced practically as low
    as desired. If observed altitude is rounded to the nearest minute, the
    error thereby injected can reach a maximum 0.5′, and half the time it's
    0.25′ or more.
    
    That can be significant if other error sources have been carefully
    minimized, the best accuracy is desired even at the cost of a little
    extra paper and pencil work, and a more accurate reduction method is not
    available.
    
    However, in ordinary navigation it's reasonable to trade the slight
    increase in error for simplified computation, and work in whole minutes.
    
    Regarding HO 211, my experiments found a 0.59′ root mean square altitude
    error. To attain that accuracy it's necessary to interpolate the table
    in some cases (less than 5%) where the mathematical leverage of the
    method is weak.
    

       
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