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<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Hello,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I am trying to understand the ”NAD27 Michigan”
datum, EPSG:6268.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>As represented in EPSG, this is a datum distinct from
NAD27,<br>
and uses the ellipsoid “Clarke 1866 <st1:place w:st="on"><st1:State
w:st="on">Michigan</st1:State></st1:place>”. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>EPSG remarks: <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> “Ellipsoid taken to be 800
ft above the NAD27 reference ellipsoid.”<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>The information source (J. P. Snyder. Map Projections:
A Working Manual, p. 56, note 1)<br>
is more precise: <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> “The major and minor axes of the
ellipsoid are taken at exactly 1.0000382 times those<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> of the Clarke 1866, for <st1:State
w:st="on"><st1:place w:st="on">Michigan</st1:place></st1:State> only. This
incorporates an average elevation throughout<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> the State of about 800 ft, with
limited variation.”<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Neither EPSG nor Snyder gives any datum shift for NAD
27 Michigan. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>However, the Michigan Department of Natural Resources
just writes:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> Datum:
NAD27<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> Ellipsoid: Modified
Clarke, 1866<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>where the ellipsoid turns out to be the same as “Clarke
1866 <st1:place w:st="on"><st1:State w:st="on">Michigan</st1:State></st1:place>”.
<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>(<a
href="http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf">http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf</a>)<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>So it seems that Michiganders regard the datum NAD27
Michigan to be the same as NAD27:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>it is not an adjustment or densification or whatever,
it just has a different ellipsoid. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>But this can be interpreted in two ways: <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> a) that long/lat are the same in both
datums,<br>
b) or that geocentric Cartesian coordinates X,Y,Z are the same in
both datums.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>If a) is intended, then a correct datum shift for
NAD27 Michigan could use the CONUS<br>
grid shift file intended for NAD27.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>And if b) is intended, then the 3-parameter shift
between NAD27 Michigan <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>and NAD27 would be 0,0,0.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>These interpretations are not quite equivalent. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I’ve tried out b) in Proj.4, by setting
identical towgs84 parameters for both datums.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>(These are not very accurate, but since they are the
same on both sides, they should<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'> cancel each other and give a 0,0,0 shift
between NAD 27 Michigan and NAD27.)<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>>cs2cs +proj=longlat +a=6378450.0475
+b=6356826.6215 +towgs84=-9,161,179 +to +proj=longlat +ellps=clrk66
+towgs84=-9,161,179<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>-85 45 0<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>85dW 44d59'59.973"N 243.235<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>So, the point at the ellipsoid surface of NAD27
Michigan is 243.235 m = 798 feet<br>
above the NAD27 ellipsoid, as expected. What surprised me is the latitude<br>
shift of 0.027" = 0.83 meters. Well, I think understand where it comes
from: the<br>
line that is perpendicular to the ellipsoid surfaces doesn’t go through
the ellipsoid<br>
center(s). But the effect is much larger than I would have thought. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>So, does anyone know whether a) or b) or something
else is the correct interpretation?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Best regards,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Mikael Rittri<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Carmenta<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Sweden<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>http://www.carmenta.com<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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