[Proj] Scale factor for Transverse Mercator

Charles Karney ckarney at sarnoff.com
Tue Sep 9 09:49:13 EDT 2008

What you mean by "scale error" is, I believe, the amount by which the
scale deviates from unity.  Whether this is an error or a problem
depends on the application.

Sure, in the standard UTM zones, the scale is close to unity and this
allows reasonably accurate distances to be computed directly.  In other
applications it may only be important that the scale does not vary much
over an area of interest (even though it's far from the central
meridian).  And the regular Mercator projection is regularly used over
large areas even though it then has a large scale variation (you
remember the variable scale on the side of the map?).  Wikipedia claims
that Google maps uses Mercator (presumably for its joint properties of
conformality and zero meridian convergence).

So I think it's incorrect to say that the TM is only "useful" +/- 3deg
from the central meridian.  You have TM algorithms which have <1um error
out to +/- 65 deg. from the central meridian.  I recommend that libproj
provide access to these and leave it to the user to decide on the

It may well be that you need to stop before 90 deg. because an algorithm
with reasonable accuracy is not available.  But here again I would hold
off on statements like "so distorted as to be unrecognizable"; locally
there is NO distortion --- the projection is conformal after all.  (By
the way, it's not the case that the TM projection on an ellipsoid
"stops" at 90deg from the central meridian; it can be extended
continuously past this point.)

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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