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On Wed 16 Jan 2002 10:07 PM in Navigation-L,
Trevor Kenchington [mailto:Gadus@ISTAR.CA] said:
> As I understand it, the various datums are different ellipsoids,
> each of which is a mathematically-perfect surface which closely
> (but not perfectly) matches the shape of the real globe, the
> early ellipsoids differing in which part of the real globe they
> most closely matched. Surely then it is not the landmarks which
> move (they, after all, are rooted on bedrock) but the positions
> of latitude and longitude lines which are defined relative to
> the particular ellipsoid?

Actually, it is the landmarks that appear to "move" between charts
with differing datums.

Underlying each datum is an ellipsoid. The ellipsoid is an idealized
smooth surface chosen to minimize differences between itself and
the geoid (a theoretical earth with all points at "sea level" and
with the surface everywhere perpendicular to the local gravity
vector) for the area covered by the datum (North America for
NAD-27) or worldwide (WGS-84).

The equator is a plane through the center of the earth perpendicular
to the axis of the poles. The prime meridian is a plane through the
poles that passes through a selected point (Greenwich). The
longitude of any other point is the angle between its meridian
(plane through the poles) and the prime meridian. The latitude is
similarly measured as the angle between the equatorial plane and
its prime vertical, a plane through the point (and the center of
the earth) and perpendicular to the point's meridian.

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.

[Diagram of lat/lon planes intersecting concentric sphere and
ellipsoid desperately needed here!]

So what's the datum shift between charts?

A plotting sheet for a given latitude gives you a place to plot
a position by lat/lon, or by reference to some other point
previously determined. A chart is a plotting sheet with landmarks
(land, shoals, channels, etc.) already plotted for you. Plotted
how?

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.
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.

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.

 -- Peter (where did my lunch time go?!)

   

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