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    Re: Sextant Positions versus Map Datums?
    From: Trevor Kenchington
    Date: 2002 Jan 17, 12:47 PM

    Peter Smith wrote:
    
    > Actually, it is the landmarks that appear to "move" between charts
    > with differing datums.
    
    I suspect that that is a matter or relative movement, in which one moves
    relative to a reference fixed to the other. If latitude and longitude
    are considered fixed, the landmarks move depending on the datum chosen.
    If the bedrock is considered fixed, the parallels and meridians shift.
    
    Since the graticule, like the datums, are only conceptual constructs
    (with a potentially infinite variety of datums to be invented, each with
    its corresponding positions for the grid of lines), I find it easier to
    consider that the bedrock is fixed for most purposes. Naturally, when
    reducing a celestial sight, it is easier to consider that the meridians
    and parallels are fixed.
    
    But that only returns us to Jared's question in another form: Which
    datum brings the drifting bedrock into correspondence with the frame of
    reference defined by the Almanac and sight-reduction tables? Since the
    landmarks move relative to the meridians and parallels depending on
    which datum is used, there must be some datum corresponding to
    celestially-derived positions and hence other datums must deviate from
    those positions.
    
    > The point to bear in mind is that lat and lon are angular measures
    > between intersecting planes. Project these planes to the stars and
    > you have celestial lat/lon, which, translated into declination and
    > hour angle, is the basis for celestial navigation. A position
    > calculated from celestial sights references these planes.
    >
    > Where these planes intersect the surface of the earth, or of an
    > earth-size sphere or ellipsoid, you have the geographic lat/lon of
    > a point. However, the difference between the lat/lon on the
    > celestial sphere and the not-quite spherical earth is vertical.
    > The planes and the angles between them remain the same. Only the
    > distance from the center of the earth changes with the surface
    > we've chosen.
    
    No. You are confusing a vertical datum (such as the datum for soundings)
    with a geodetic datum, which is a reference for horizontal position (See
    the discussion in Bowditch).
    
    The positions of landmarks on the (irregular) surface of the Earth must
    be projected onto the ellipsoid for a particular datum in order for its
    latitude and longitude to be determined. Change the ellipsoid and you
    will change the point at which the projection intersects it.
    
    > Each horizontal datum begins with a set of reference points whose
    > lat/lon is determined as accurately as possible. From these
    > reference points, ancient or modern surveying methods are used to
    > assign latitude and longitude to other landmarks, and you have a chart.
    
    That is the process of constructing a geodetic grid. The measurements
    thus obtained still have to be reduced to datum -- mathematically
    projecting them onto the chosen ellipsoid.
    
    > Newer datums have more accurately determined base references and
    > more accurate surveys from them. But it's not the underlying
    > latitude and longitude that shifts between datums, its the assignment
    > of lat/lon to landmarks.
    
    No. WGS83 involves a different ellipsoid from those used previously --
    selected to be a good approximation to the true shape of the Earth
    everywhere, now that GPS allows high-precision global navigation.
    Re-drawing charts to WGS83 caused the apparent latitudes and longitudes
    of their landmarks to change without any new geodetic or other surveying
    being done.
    
    > Thus, if you take a lat/lon and plot it on charts with two different
    > datums, it's still the same lat/lon on both, but the distance and
    > bearing from that lat/lon to a given landmark may change. Likewise,
    > a landmark, or a point determined by range and bearing from it may
    > plot at different lat/lons on the two charts.
    
    There I think you are confusing yourself over relative motion. Yes, your
    latitude and longitude remain numerically the same regardless of which
    chart you plot them on. However, your plotted _position_ would not be
    the same relative to the solid crust of the Earth. Your distance and
    bearing from the nearest lighthouse would be different (and the
    lighthouse would not have left its foundations).
    
    
    So what is the answer to Jared's question?
    
    Most of the data in the Almanac relates only to angles relative to the
    planes of the Equator and the Prime Meridian, and so are equally
    applicable to all regular ellipsoids, or else (as with semi-diameters)
    they are values that are effectively independent of the shape of the
    Earth. Dip should be affected by differences in the local curvature of
    the Earth but our planet's deviations from sphericity are never enough
    to worry about that. Maybe the horizontal parallax correction would be
    affected by choice of datums. I am not sure.
    
    When it comes to sight reduction, Ageton's tables are based on spherical
    trigonometry and thus must assume that the Earth is a perfect sphere
    (or, more precisely, that the observer is on the surface of a perfect
    sphere centred at the centre of the Earth). Even HO 229, which could
    have values separately calculated for each latitude (though not for each
    longitude) and so could be adapted to some ellipsoids, is calculated
    strictly by spherical trig. (see the computation formulas in Section E.
    BACKGROUND of each volume).
    
    Thus, while more than willing to be corrected by those with a deeper
    understanding, I still suggest that positions calculated from celestial
    observations are suited to an assumed spherical Earth and so do not
    exactly match _any_ geodetic datum.
    
    The error (relative to any local or global datum) will be tiny compared
    to the effects of observational errors, of course. However,
    sight-reduction computations with HO 229 have a maximum error of 0.05
    minutes of arc. For comparison, in my area the difference between NAD27
    and NAD83 is some  2.5 seconds of arc (0.04 minutes) and the difference
    between either and a perfect sphere is likely to be larger. Thus, the
    error due to differences in datum between celestial calculations and
    charted objects is only just beyond the limits of concern to the navigator.
    
    
    Another reason not to rely on celestial fixes when in coastal waters.
    
    
    Trevor Kenchington
    
    
    --
    Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
    
                        Science Serving the Fisheries
                         http://home.istar.ca/~gadus
    

       
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