I am trying to understand the ”NAD27 Michigan”
As represented in EPSG, this is a datum distinct from
and uses the ellipsoid “Clarke 1866 Michigan”.
“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
Neither EPSG nor Snyder gives any datum shift for NAD
However, the Michigan Department of Natural Resources
where the ellipsoid turns out to be the same as “Clarke
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
b) or that geocentric Cartesian coordinates X,Y,Z are the same in
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
-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
line that is perpendicular to the ellipsoid surfaces doesn’t go through
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?