I have CAD files which were created in a "Staten Island local datum". There is no spatial information associated with these files, just annotation mentioning the datum. After researching this datum, I discovered that it's origin is located at N 137,190.02, E 1,967,746.81, according to the NAD_1927_StatePlane_New_York_Long_Island_FIPS_3104 coordinate system.
Given this info, how do I get these files to line up with the rest of my data? Do I need to create a custom projection?
I solved this essentially following the instructions from mkennedy here: Create custom projection using either QGIS or ArcGIS Desktop?
I found the .prj file for NAD_1927_StatePlane_New_York_Long_Island_FIPS_3104, and modified the false easting and westing until my data lined up.
Original 1927 NYLI State Plane: PROJCS["NAD_1927_StatePlane_New_York_Long_Island_FIPS_3104",GEOGCS["GCS_North_American_1927",DATUM["D_North_American_1927",SPHEROID["Clarke_1866",6378206.4,294.9786982]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Lambert_Conformal_Conic"],PARAMETER["False_Easting",2000000.0],PARAMETER["False_Northing",100000.0],PARAMETER["Central_Meridian",-74.0],PARAMETER["Standard_Parallel_1",40.66666666666666],PARAMETER["Standard_Parallel_2",41.03333333333333],PARAMETER["Latitude_Of_Origin",40.5],UNIT["Foot_US",0.3048006096012192],AUTHORITY["EPSG",4456]]
Modified custom projection: PROJCS["Staten_Island_Local",GEOGCS["GCS_North_American_1927",DATUM["D_North_American_1927",SPHEROID["Clarke_1866",6378206.4,294.9786982]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Lambert_Conformal_Conic"],PARAMETER["False_Easting",11898.0],PARAMETER["False_Northing",-57566.0],PARAMETER["Central_Meridian",-74.0],PARAMETER["Standard_Parallel_1",40.66666666666666],PARAMETER["Standard_Parallel_2",41.03333333333333],PARAMETER["Latitude_Of_Origin",40.5], UNIT["Foot_US",0.3048006096012192]]
FYI - PolyGeo's answer would have worked if I had even one projected CAD file to base a custom projection. Unfortunately, I didn't have this.
If you need to create a custom coordinate system then there is an Esri How To: Create a custom projection file to align CAD Data in ArcMap 10.1 and above that should be useful:
The instructions provided describe how to create a custom projection file for CAD data, and how to align the CAD file with other data in a projected coordinate system with units of feet, meters, or other linear units in ArcMap 10.1 and above.
