[Proj] Need help to verify if cs2cs results are correct.

[Byeong Kim]

Hi all,
 
I am trying to figure out the possible displacement by using a Lon/Lat
pair mistakenly. Suppose we have a coordinate based on Clarke1866 (in
ESRI's term it is GCS_Assumed_Geographic_1). This ellipsoid can be found
in many US Census data. If someone uses this pair as if it is based on a
Perfect Sphere (likely R=6370997.0m), what's the possible error in (X,Y)
by Lambert Conformal Projection? That's what I am trying to figure out.
So, I wrote a BAT file (I am using a PROJ.4 utilities on XP by compiling
it with MinGW and datum shift tables) to compute it. Steps are
following: I assume that the given value is based on Clarke1866. So I
transformed it into a Lat/Lon on a Perfect Sphere. Then I performed LCC
projection for both pairs.
 
----------------------------------------------------------------------
@cs2cs +proj=longlat +ellps=clrk66 +datum=NAD27
+towgs84=-3,142,183,0,0,0,0 +to +proj=latlong +ellps=sphere +R=6370997
+towgs84=0,0,0 +no_def -f "%%f2" -w9 MonLonLat >
MonLonLat.Clarke1866ToSphere
@cs2cs +proj=longlat +ellps=clrk66 +datum=NAD27
+towgs84=-3,142,183,0,0,0,0 +to +proj=latlong +ellps=sphere +R=6370997
+towgs84=0,0,0 +no_def -f "%%f2" -w9 MonLonLat 
@proj +proj=lcc +lat_1=60.0 +lat_2=30.0 +lat_0=40.0 +lon_0=-100.0
+x_0=0 +y_0=0 +ellps=sphere +R=6370997 -f "%%f2" -w9  MonLonLat
@proj +proj=lcc +lat_1=60.0 +lat_2=30.0 +lat_0=40.0 +lon_0=-100.0
+x_0=0 +y_0=0 +ellps=sphere +R=6370997 -f "%%f2" -w9 
MonLonLat.Clarke1866ToSphere
----------------------------------------------------------------------
I added a duplicate cs2cs line just because to print out the result of
first line on screen as well as to store in a file.
 
The file "MonLonLat" has this value
-84 33. 0
 
Then I got these outputs. 
-84.0000002     32.8244522 834.0192882  ==> it is also stored in
MonLonLat.Clarke1866ToSphere
1464716.5725192 -614514.0442942 0
1468546.7535622 -633426.1117132 834.0192882 ==> by using
MonLonLat.Clarke1866ToSphere
 
The first line indicating that no serious shift in Lon value as we can
expect. But the lat value comes out significantly different then the
original value and it ended up about 20 km difference!
 
Is anyone willing to confirm that PROJ4 gives the correct answer to my
question? Thank you.
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