Re: Expanation of datum/grid terms requested

From: David Lee (davidlee_malvern_at_dont.use.this.bit.hotmail.com)
Date: 06/22/04 

Date: Tue, 22 Jun 2004 13:15:30 +0100

Vincent van der Laan wrote...
> I live in Holland and I found the following recipe to enter our Dutch (RD)
> grid and datum in my Magellan MeriPlat:
>
> From the Position Screen take Menu Coord System and give an [enter].
> There is a choice now: Primary of secundary [enter]
> User Grid [enter]
> Projection => Trans Merc [enter]
> Latitude of origin = 52.15617N [enter]
> Longitude of origin = 005.38763E [enter]
> Next > [enter]
> Scale factor = 0.99990790 [cursor]
> Units to meter conversion = 1.00000000
> False east at origin = 00155000.0
> False north at origin = 00463000.0
> Done [enter]
>
> Then the next things:
>
> Map datum [enter]
> primary of secundary [enter]
> USER [enter]
> Delta A (meters) = +0740.000 [cursor]
> Delta F (meters) = +0.10037480
> Delta X (meters) = +593.0
> Delta Y (meters) = +0026.0
> Delta Z (meters) = +0478.0
>
> It works!
>
> But now I am very curious about all these technical terms; what do all the
> above parameters mean? I can figure out "Latitude of origin" and
"Longitude
> of origin", but that's about it!

Seeing as no-one else seems to have answered I'll try to answer as far as I
understand...

The five 'delta' parameters are used to convert between the WGS84 reference
ellipsoid used by the GPS system and the ellipsoid used by your local
mapping. Whilst WGS84 is a good average fit to the whole world it doesn't
give a good fit in any particular place and the local fit varies with time
(eg upto 10cm per year in Hawaii). WGS84 is geo-centric. On the other
hand your local datum will only be a good fit locally and it could be
centred anywhere.

Delta A gives the difference between the major (I think) axes of the two
ellipsoids and Delta F is the difference between the two ratios of major and
minor axes (ie the 'flattening' compared to a sphere). Delta X, Y and Y
account for the difference in the centres of the two ellipsoids.

The other parameters define your local Cartesian coordinate system.

Trans Merc means Transverse Mercator - basically the surface features of a
globe are projected onto a flat map wrapped cylindrically around such that
it touches noth north and south poles (that is your local grid north and
south). (Mercators original projection used a cylinder wrapped around the
equator).

Latitude and longitude of origin define the reference point to which the
mapping is related - this longitude is the line in contact with the cylinder
and is the only line where there is no distortion of the projected map.

Because you can't flatten the surface of a sphere without stretching it,
distances on the map will be exaggerated as you move away from the principal
longitude. Hence a small scale factor is applied so that the average scale
is correct over the area of the map, which minimizes the maximum scaling
error.

Units to meter conversion is obvious - one unit in a full grid reference
represents one metre

The false origin is just the point where the measurement of practical
coordinate system is based, to ensure that the usable map starts at 0,0 and
there are no negative grid references. False North and East simply define
where this point is relative to the actually origin of the map projection.

Hope that this helps (and I haven't made any terrible errors!)

David

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