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    Re: typical standard deviation?
    From: George Huxtable
    Date: 2009 Aug 12, 10:56 +0100

    Jeremy has properly questioned an assertion I made in [9435] about the moon
    data-set he provided in [9359]
    
    I wrote-
    "The deduced scatter, of one standard deviation about the fitted trendline,
    I now make to be 0.53 arc-min in the case of the "Moon near LAM" set, and
    0.38 arc-min in the case of the "Moon away from LAM" data set. That's no
    better, and no worse, than one would expect from observations at sea from a
    large vessel."
    
    He commented-
    "I wonder on what basis this statement is made.  I am not claiming to  be
    any better or worse, than any other practiced navigator, but how can we know
    "somewhere around 0.5 arc-min is what "...one would expect from observations
    at  sea from a large vessel.  Is there some collection of data that would
    back  this up?  I am just wondering how we can expect this kind of deviation
    from  large ships as opposed to small vessels unless there has been some
    sort of study  on ships of various sizes and under different observing
    conditions or a review  of a variety of navigational logs.
    Can any other navigator on this list give data that would support this kind
    of statement, even if the data isn't recent?"
    
    =====================
    
    That's a fair question. I should explain that I had previously stated, in
    [9412], that-
    
    "A least-squares fit to the non-culminating series arrives at a rms scatter
    of little more that 0.1 arc-minute, and of the series aroundculmination of
    about 0.15 arc-min. ....  they show what can be achieved by a careful
    observer on a large vessel in, presumably, benign conditions."
    
    I had indeed been rather surprised by that conclusion; as well I might,
    seeing that it had resulted from a silly spreadsheet error, as I pointed out
    later (I had put a comma in a formula, where it should have been a colon.).
    I expect those low values for rms scatter may well have surprised Jeremy,
    also.
    
    However, with that error corrected, the revised scatter became about four
    times greater, and my comment about that was really intended to say no more
    than- "now, that looks more like a reasonable value". Which it does, as I
    suspect Jeremy would agree. Perhaps it would have been wiser to say no more
    than that. I can offer no direct evidence of what would be a reasonable
    range of horizon scatter, from a bridge over 100ft high in various
    conditions. Jeremy's opinion would be more valuable than mine. In what range
    would his own estimates lie, in various conditions, I wonder?
    
    I agree with almost every word of Jeremy's statement-
    
    "The reason I bring this up is that as I look through my recent navigational
    log, I notice that the most critical aspect of shooting a star is seemingly
    never mentioned (at least far less than sea state, large ships, and
    anomalies in  dip).  This factor is the quality of the visible horizon!
    The horizon varies with time, azimuth, and circumstance every time I  shoot.
    I have shot with a crisp horizon in one direction, and a fuzzy  horizon in
    another quadrant at essentially the same time.  The  horizon's quality at a
    given azimuth, affect my sights far more than any other  shooting condition.
    The quality of the horizon greatly changes the  accuracy of my star fixes
    which is the only measure I truly care about."
    
    Qualty of horizon is indeed crucial, and often neglected. I remember
    suggesting to Jeremy, in one posting some time ago, to improve on a hazy
    horizon by following  Lecky's advice and descend from his lofty bridge, with
    its 12-mile horizon distance, to a lower deck level, from which the horizon
    would get much closer and sharper. Lecky would occasionally observe by going
    over the side to the foot of the accommodation ladder, which is rather more
    than I would expect Jeremy's Captain to allow.
    
    When we compare altitude observations from big ships and small boats, vessel
    size does much more than reducing the amount the observer gets thrown about.
    It has two major effects on the scatter of the horizon.
    
    From my own cockpit, the horizon is only 3 miles away, so it's much less
    often spoiled by haze than would happen to Jeremy. In that respect, the
    small vessel has the advantage.
    
    On the other hand, when surrounded by waves and swell that can be greater
    than the observer's height-of-eye, and affected by heave to a similar
    extent, a small-boat navigator can find himself looking sometimes up at the
    wave-peaks that surround him, sometimes down. That can be minimised, to an
    extent, by sighting to surrounding wave-peaks when the craft is at the top
    of its heave, but it's still a chancy business in rough conditions. By
    contrast, Jeremy will always see a horizon that might have been drawn with a
    ruler. Even though his ship may roll, that won't affect altitudes
    significantly, and the effect of any heave will be negligible. In rough
    conditions, all the advantages lie with the big-ship.
    
    He ended "Given the nearly endless variations of observing circumstances for
    any sight using the visible horizon rather than a bubble or other artificial
    horizon, I find it hard to justify stating in all but broad terms what
    magnitude of scatter we can expect from a given type of vessel."
    
    I agree.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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