[Proj] Geocentric vs. Geodetic latitude

[Clifford J Mugnier]

The use of geocentric latitude has had only one valid geodetic application
in the past century of which I am aware.  The most common application
(nowadays) of geocentric latitude is for thematic cartography applications
where the Earth is considered a sphere and the accuracy of the coordinate
data is no better than a kilometer or so.  Many geographers couldn't care
less about the ellipsoid, so that's what they use.

The valid geodetic application I speak of was discovered by John P. Snyder.
John discovered that the old North American Datum of 1927 State Plane
Coordinate System Projection Books (the blue ones) for each state were
computed "wrongly."  Instead of using the conformal latitude for the
computation/construction of the lookup tables (for the Lambert Conformal
Conic), the U.S. Coast & Geodetic Survey computed GEOCENTRIC latitude
instead.  The reason was the difference was quite minor for the accuracy of
second-order transit/tape surveys (back then only 1:10,000 closure), and it
would not make that meaningful a difference in the computed Lambert
Conformal Conic coordinates AT THAT TIME (1930s).

When Charles N. Claire came out with his Special Publication No. 62-4,
"State Plane Coordinates by Automatic Data Processing," he implemented
special "fudge factors" in the coefficients to enable the duplication of
the screwy geocentric latitude results for the Lambert Conformal Conic
projection transformations in the U.S.  The numerical precision of the
mini-computers of the day were greater than the mechanical calculators, and
Claire needed to make the coefficients "compatible" with the old hand
computation results from the old "blue books."

And that, boys and girls, is the ONLY valid geodetic application of
"Geocentric Latitude" that I have ever heard of, and it was John P. Snyder
that told me about it.

Cliff Mugnier
LOUISIANA STATE UNIVERSITY