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    Re: sight reduction tables
    From: George Huxtable
    Date: 2007 Oct 2, 19:29 +0100

    Ronald van Riet wrote-
    
    | I am a relative newcomer to the celestial navigation arena so forgive
    | me if what I say has been said a zillion times before or makes no
    | sense at all,
    
    No need to apologise, that contribution is relevant and perceptive.
    
    but George points out (rightly it seems) that there can
    | be large errors in azimuth with an example where the azimuth is up to
    | 15 degrees off.
    
    With that particular azimuth table, yes, under certain circumstances, it can
    be, but even there, in most cases the errors will be much less than that.
    
    | Why is that so bad? By how much does that displace the resulting LOP
    | and the fix using one or two more LOPs?
    
    It's quite true that in most cases, azimuths are not required to great
    precision, which is why I wrote-
    
    "It's true that as long as intercepts are kept short, by a good guess at the
    DR position, no great precision is called for in azimuths." For most
    applications, a precision to a degree or two (as had been claimed) would be
    perfectly acceptable. If intercepts are kept within 60 miles then an error
    of 1 degree will give rise to an error in plotting the result of the order
    of a mile or so. Few navigators would be concerned about that. Precise sight
    reductions, such as HO 214 and HO 229, give azimuths to 0.1 degrees, but for
    most of us this is overkill, though for special purposes, such as precise
    compass-checking, it could have its uses.
    |
    | And if you want to be more precise, why not use the new fix as the
    | assumed position for a next round of calculations? Since this AP would
    | be much nearer the actual position, an azimuth offset by 15 deg won't
    | make any significant difference.
    
    That's true. Indeed, the St Hilaire method of finding position is really an
    iterative one, that starts with a rough guess and gets you much closer to
    the truth, though it's rarely taught in those terms. So you can get shorter
    intercepts, and a better result, by taking a calculated position as your DR,
    and going round the loop once again. Though hardly anyone ever does.
    
    In what circumstances would you recalculate? You might decide, in advance,
    that because of distrust of the calculated azimuths, you will always go
    round the loop twice. That would be doubling your workload, in when in most
    circumstances it would be unnecessary. Or you might decide to recalculate
    only when you found a suspiciously large error-triangle (cocked hat). But if
    that triangle resulted from scatter in the initial observations,
    recalculation would not improve matters.
    
    But there's another problem. Usually, calculation using sight-reduction
    tables called for an assumed position, that differs from your DR by being at
    integral degrees in latitude, and with a LHA that's also in integral
    degrees. In which case, reiteration can get intercepts down to 30 miles or
    so, but not further.
    |
    | Then again, if we know under what circumstances the error is large,
    | why not shoot some celestial objects that do not exhibit these large
    | errors? assuming of course, that these are available.....
    
    Well those errors in the azimuths occurred at rather unexpected spots in the
    tables, though always in a generally Easterly or Westerly direction. You
    would need to somehow make a survey of that azimuth table to discover the
    bad-spots to avoid, and that sounds unfeasible. Otherwise, if you chose to
    avoid all sights within, say 20 degrees of due East or West, that may be
    safe. But that would exclude many otherwise-useful sights, taken in the best
    direction for determining longitude.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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