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    Re: Bowditch Table 15
    From: George Huxtable
    Date: 2005 Jan 24, 22:21 +0000

    Trevor Kenchington wrote-
    
    >I am gradually working my way through Bowditch (1995 edition), trying to
    >be sure that I understand everything that is relevant to smaller vessels
    >that the book is really intended for. Most I can follow, sometimes with
    >a bit of effort, but I am having trouble with Table 15. Since the table
    >numbers have changed between some editions, Table 15 in 1995 was the one
    >providing "Distance by Vertical Angle Measured Between Sea Horizon and
    >Top of Object Beyond Sea Horizon". (That was Table 9 in at least one
    >edition of Bowditch.)
    >
    >The text description accompanying the table says that it provides the
    >distance to the object (by implication: from the observer to the
    >object), given a knowledge of the difference in height between the
    >observer's eye and the object, plus a vertical angle measured between
    >the top of the object and the horizon (that angle being corrected for IE
    >and dip). [The Bowditch main text doesn't seem to refer to Table 15 and
    >mixes this business of an object beyond the horizon with the common
    >business of distance off by vertical angle of an object of known height
    >whose waterline is visible.]
    >
    >Table 15 itself does give distances from observer #1 to the object
    >observed, if the observer #1 has zero height of eye and the top of the
    >object is just dipping below the horizon. At least, the tabulated
    >distance then equals the horizon distance for an observer (#2) at the
    >top of the object, which should be the same thing.
    >
    >However, if Table 15 was to be believed, as observer #1 climbs the mast
    >of his boat and increases his height of eye, the object observed would
    >drop below his horizon (assuming its true distance did not change),
    >which is obviously nonsensical.
    >
    >So ... if Table 15 does not give the distance from observer to object,
    >except in special cases, what does it provide?
    >
    >I'm guessing that it might be the distance from the object to the
    >observer's horizon, to which the observer's horizon distance must be
    >added to get the full distance from observer to object. However, I do
    >not know of any way to either confirm of refute that idea (save for a
    >full-scale experiment, which is a bit beyond my resources just now).
    >
    >
    >Can anyone sort this out for me?
    
    ===========
    
    Trevor has presented us with an interesting little problem about Table 15
    in Bowditch (in vol 2 of my 1981 edition, it's Table 9).
    
    It took rather a lot of pondering time, but in the end my conclusion is
    that Bowditch has got it right.
    
    Where Trevor has got things wrong is in saying-
    
    >However, if Table 15 was to be believed, as observer #1 climbs the mast
    >of his boat and increases his height of eye, the object observed would
    >drop below his horizon (assuming its true distance did not change),
    >which is obviously nonsensical.
    
    This is because the angle tabulated in that table is not, actually (despite
    the title and the table-heading) the angle of the distant object above the
    observer's horizon. It would be, except that in the accompanying text (not
    on the same page as the table), the user is told to correct the observed
    elevation, not just for index error, but also for DIP! Trevor has
    recognised this, in quoting "(that angle being corrected for IE and dip)".
    
    So the angle in the table is then the elevation of the distant body above
    the observer's LOCAL TRUE HORIZONTAL, not the angle above his local
    HORIZON.
    
    When the observer climbs his mast, the increasing dip causes an increasing
    depression of the local horizon, so the distant object protrudes more above
    it, as Trevor correctly says. But he has to correct that measured elevation
    for the increasing dip, and the resulting corrected angle, above his true
    horizontal, will now shrink (very) slightly as his height of eye increases.
    Which is just as one would expect.
    
    It's very naughty of Bowditch, however, to head that table "Distance by
    Vertical Angle Measured Between Sea Horizon and Top of Object Beyond Sea
    Horizon" (which it isn't, really), without noting on that page the
    importance of first correcting that measured angle for dip. To discover
    that instruction, one has to look in the "explanations" for that table,
    over 100 pages further back.
    
    I bet Trevor isn't the first navigator to be puzzled by the way that table
    is presented.
    
    George.
    
    
    ================================================================
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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