[Proj] How does the datum "NAD27 Michigan" work?

[Mikael Rittri]

Hello,
I am trying to understand the "NAD27 Michigan" datum, EPSG:6268.

As represented in EPSG, this is a datum distinct from NAD27,
and uses the ellipsoid "Clarke 1866 Michigan".
EPSG remarks:

    "Ellipsoid taken to be 800 ft above the NAD27 reference ellipsoid."

The information source (J. P. Snyder. Map Projections: A Working Manual, p. 56, note 1)
is more precise:

   "The major and minor axes of the ellipsoid are taken at exactly 1.0000382 times those
    of the Clarke 1866, for Michigan only. This incorporates an average elevation throughout
    the State of about 800 ft, with limited variation."

Neither EPSG nor Snyder gives any datum shift for NAD 27 Michigan.

However, the Michigan Department of Natural Resources just writes:

      Datum:    NAD27
      Ellipsoid: Modified Clarke, 1866

where the ellipsoid turns out to be the same as "Clarke 1866 Michigan".
(http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf)

So it seems that Michiganders regard the datum NAD27 Michigan to be the same as NAD27:
it is not an adjustment or densification or whatever, it just has a different ellipsoid.

But this can be interpreted in two ways:
   a) that long/lat are the same in both datums,
   b) or that geocentric Cartesian coordinates X,Y,Z are the same in both datums.

If a) is intended, then a correct datum shift for NAD27 Michigan could use the CONUS
grid shift file intended for NAD27.
And if b) is intended, then the 3-parameter shift between NAD27 Michigan
and NAD27 would be 0,0,0.

These interpretations are not quite equivalent.

I've tried out b) in Proj.4, by setting identical towgs84 parameters for both datums.
(These are not very accurate, but since they are the same on both sides, they should
 cancel each other and give a 0,0,0 shift between NAD 27 Michigan and NAD27.)

>cs2cs +proj=longlat +a=6378450.0475 +b=6356826.6215 +towgs84=-9,161,179 +to +proj=longlat +ellps=clrk66 +towgs84=-9,161,179

-85 45 0

85dW    44d59'59.973"N 243.235

So, the point at the ellipsoid surface of NAD27 Michigan is 243.235 m = 798 feet
above the NAD27 ellipsoid, as expected. What surprised me is the latitude
shift of 0.027" = 0.83 meters. Well, I think understand where it comes from: the
line that is perpendicular to the ellipsoid surfaces doesn't go through the ellipsoid
center(s). But the effect is much larger than I would have thought.

So, does anyone know whether a) or b) or something else is the correct interpretation?

Best regards,

Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com

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