[OSM-talk] Datums again?

[Nick Black]

A spherical model of the earth is not suitable, simply because the
earth is not a sphere.  The earth is infact an ellispsoid of rotation
- it is fatter in the middle  - like taking a footbal (soccer ball)
and sitting on it.  Using spherical geometry in this instance, will
result in distortions that increase as you move further away from the
equator.

To get around this problem, the earth can be modelled as an ellispse -
this is done by calculating a flattening ratio.  This is why
calculations based on differnent appoximations of the ellipse give
different resutls (lat and lons).  Ellipses are the thigns called
Clarke 1880, or Airy 1830 or WGS 84.  They best approximate the earth
in the region they were derived.  Datum shifts are further complicated
because each country or agency moves its ellipse to fit the earth
better and to minimize local distortion.  WGS84 is designed for the
entire world, so its a best effort  - one that minimizes errors
everywhere, but is not perfect anywhere.

Then things get even more complicated.  The ellipse is ok - but if you
want to use a Differential GPS or something flashy that measures to cm
accuracy, and you want to measure over a long distance, say to build a
railway line accross America, the distortions in the earths surface
would not be adequately modelled by the ellipse.  This is all to do
with gravity and the idea of horizontal - the equipotenial plane -
which is the reference from which vertical is measures.  Gravity as a
force acts towards the centre of mass, which is pretty much the centre
of the earth.  But, irregularities in the Earth's crust cuase
variations in the earth's gravitational field.  This distorts the
vertical datum at different points on the earth's surface.  So if you
use an ellipsoidal model, and you measure the angle between vertical
on the equator and vertical and 40 degrees lat - it wont acutally be
40 degrees - it will be 40.0000001 or something - bad news for
precision engineering.  This is because of the different gravitational
attractions at each point.

So to counter this, we measure the differing gravitational attractions
at variuos points, interpolate between them, and make a nice picture
like this:

http://www.geos.ed.ac.uk/research/subsurface/geoid.jpg

Which results in bitch equations that no one can be bothered to use -
so we just use OSGB36 with the Airy ellispsoid.  The high accuracy
model for the UK is OSTN02 - which is *I think* what MasterMap is
referenced to

http://en.wikipedia.org/wiki/Geodesy
http://en.wikipedia.org/wiki/Geoid

On 1/19/07, Andrew Rowbottom <andrew.rowbottom at gmail.com> wrote:
> in response to
>
> >Can anyone explain why a simple spheric model is not sufficient?
> >Does it result in cracks somewhere on the planet?
> >Are lat and lon coordinates incorrect for someone's street somewhere?
> >Is the distance between two points distorted in some way?
>
> Q1 I'm not answering this one (cop out!)
> Q2 It's be a bit clearer if it did.
> Q3 look at http://gps.ordnancesurvey.co.uk/guide1.asp it surprised me
>     also the image at
> http://www.colorado.edu/geography/gcraft/notes/datum/gif/shift.gif
>    show how the "datum" aka non spherical earths can affect positioning.
> Q4 The distance is indeed distorted... because the earth isn't
> spherical the on the ground distance isn't the same (even if the world
> was all water with no moon)
>
> On the other hand there are so many possibilities I think we should
> pick one, pragmatically WGS84 seems to be a de-facto standard.
>
> Andrew Rowbottom
>
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-- 
Nick Black
--------------------------------
http://www.blacksworld.net