[Proj] Scale factor for Transverse Mercator

[Gerald I. Evenden]

On Wednesday 10 September 2008 11:39:31 am Charles Karney wrote:
> Gerald I. Evenden <geraldi.evenden at gmail.com> wrote:
> > Let me pose the question: why are all of the state plane zones in the
> > US established to have very small scale errors (factors) over their
> > extent?
>
> Because an important application for state maps is defining land
> ownership, building roads, etc.
>
> > Why did DOD create the 6 degree zone if it were not to minimize the
> > scale error.
>
> DOD also wants bullets to go predicable distances in straight lines on
> maps.

Indeed, but in a sense this is also the same reason for the state plane 
system---a mechanism to apply Cartesian mechanics to measurement problems.  I 
must add that military usage is also dependent upon a wide level of mental 
capability among the grunts on the ground and combined with the fog of war it 
is a little easier to deal with these problems in Cartesian coordinates.  It 
should probably be added that today's electronic warfare probably has a great 
deal of effect on how maps are used in a modern combat---UTM is a relic of 
mid 20th century warfare technology.

> However, both these applications are concerned with a subclass of human
> activities close to the surface of the earth.

To be sure.  But when we go to smaller scale we are more interested in 
thematic mapping where we are less intersted in "measuring" in a 
ruler-compass sense but visually understanding the "layout" of information.  
It is in this usage that I am much more in favor of equal area maps because I 
feel that the sense of areal extent is much more important than conformality.  
The human eyeball does not really care if the graticule lines meet at right 
angles everywhere.

> Google maps' use of Mercator is different class of application.  The
> requirements here are conformality and seamless scrolling over most of
> the globe with the normal application being navigating on roads rather
> than plotting great circle routes between continents.  Here the
> much-maligned Mercator seems to be an appropriate choice.

For what google is doing the projection makes little difference.  The roads 
are probably in arc-node data sets where the distance along road segments 
(arcs) are a matter of the data set and have nothing to do with the map 
projection.  If they are using Mercator, they would probably adjust the 
latitude of true scale as the latitude of the region displayed changes,  Thus 
the "smooth" transition aspect is void.  If they didn't adjust lat_ts then a 
street map of Brownsville, TX would look odd compared to a street map of 
Fairbanks, AK or vice versa.

Another minor point with google, I bet they are *not* using a elliptical 
projection software.  If they are, they are wasting a vast amount of computer 
time.

> I also read with interest Dozier's remark in NOAA Technical Report NESS
> 81 that the TM projection (extended beyond +/- 3deg) is useful for
> analyzing data from the NOAA A-G series of satellites.  I don't know why
> this might be beyond my ascertaining that these satellites are in polar
> orbits and TM can at least handle a single such orbit seamlessly.  So
> here is an application unanticipated (probably) by Gauss for the TM and
> beyond the narrow question of how to get a good map of Hanover.

There are lots of special projections in handling problems unique to 
satellites.  Even in a polar orbit the path is not N-S on the map because the 
earth turns as the satellite passes over head.

> I guess my point is that a library offering general-purpose projection
> capabilities should being agnostic on questions of what is a "good"
> projection.  Such issues are really in the application domain.

The question is not a moral question of good or bad but what is relevant.  
Sure, use TM beyond the 6 degree zone but don't mistreat it like Mercator and 
make a world map out of it.  In addition, do not waste cpu clicks by using 
the ellipsoid form when performing this extension.  If there is a moral issue 
then it may be to *not* develop TM to 90/0 or to make the usage so costly 
that it is never performed and thus minimize the carbon footprint of 
cartographic projections.   :-)
-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist