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    Re: Round-off
    From: Peter Fogg
    Date: 2009 May 16, 18:20 +1000
    John Karl writes:
    I wasn't talking about sailing risk.  
     " I'm not satisfied to miss reefs only a percentage of
    the time.
    "
    But rather, I was addressing
    round off error in sight reductions.  
    Yes, me too.
    Certainly in some circumstances
    (such as learning, navigating in the open ocean, or lifeboat
    situations) large uncertainties (like 10 miles or even more) are quite
    acceptable.  But when Cnav is really important why introduce
    unnecessary uncertainties in the sight reduction??
    The main reasons for lack of accuracy, from the deck of a small boat at any rate (the sort of craft I'm assuming you'd be aiming to miss reefs from) is the unstable nature of that platform, difficulties with identifying and using the horizon, anomalous refraction (related to the minimal elevation), etc.  Given those practical restrictions, getting a fix within 10nm of your position could be quite a reasonable result.
    In these conditions great refinement of the sight reduction process may have no practical benefit to offer.
     Why add more to
    the inherent uncertainty in the observation??  
    Using rounded values may offer a practical benefit of computational simplicity.  The statistical reality is that these rounded values do not tend to accumulate.  On the contrary, the differences tend to cancel each other out.  Frank recently (and others in the past, its not the first time this topic has arisen) has outlined precisely how error accumulates, as a formula. What I'm stating here is the practical result.
    Using H.O. 229 or a 10-
    digit calculator and maintaining 0.1' arithmetic should produce a
    sight reduction accurate to about 0.5'.  
    If your sights have such inherent built-in potential observational inaccuracy (ie; scatter), for the reasons above, then your sight reduction to that level of precision is not going to improve them.
    However, remember Almanac
    data is only guaranteed to 0.25 for the sun and 0.3' for the moon.
    And even when double second difference interpolation is required in
    H.O. 229, that table's accuracy can drop to 0.3', further adding to
    the uncertainty.  So in some cases, exclusive of observational error,
    the sight reduction itself can have an error of up to 0.8'.
    Rounding of values may have little to commend it in situations where maximum accuracy is sought, and circumstances indicate little observational scatter is likely.  Its simply a case of horses for courses.
    Even in keeping statistics to evaluate observational skill, one needs
    to minimize the arithmetic error in the sight reduction calculation,
    and needs to know just what that uncertainty is.
    Actually, what is really useful are methods to reduce:
    1.  Erratic error - the sort you are likely to get from a pitching deck when its a struggle to see the horizon, read the watch or the sextant correctly etc.
    2.  Systemic error - consistent time or instument error, etc.
    Applying the relevant techniques to correct for each, in the order above, can offer real practical improvements in accuracy. 
    This has been much discussed here in the past.  If you are interested in searching our archives, "slope" will find you much material relevant to 1, and variations of 2 (systematic error, etc) may assist there.
    These techniques also have much to offer those seeking maximum accuracy, eg; those using a theodolite.  Variations were taught to surveying students, in the days when they still learned Civil Astronomy.



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