So I wanted to determine the geographical center of Lorain County Ohio. I didn’t find it online at first so I decided to calculate it myself. I have various maps at hand from the Ohio Dept of Transportation printed out that I mark up with various things. I picked a printout about 16" high and cut it out carefully then used the old school method of establishing it with plumb lines. Despite the grade school feel of this method it is an actual geometrically correct method.
It’s a nice shape for this method with 8 different corners to hang it from. I used a thin pin and hung it on the wall and let it stabilize then hung a plumb bob made of a very thin thread with a washer on the end and traced the relevant sections onto my paper map. They all converged with excellent precision at one point. I used various landmarks and a ruler to transfer this point onto a Google map to determine the latitude and longitude. I got 41.2998, -82.1571, great!
But then I did manage to find it listed on this page:
They claim it is at 41.3149, -82.1561
This is more or less on the same longitude but one mile north in latitude compared to my measurement. On my paper map that comes out a half inch further north but on the same vertical line.
I’m trying to figure out what I did wrong? If I were to bias my paper map to make it work out I would have to add about a 1 inch strip along the shoreline to pull the centroid north a half inch. I doubt that my ODOT map is off that much.