If you take the road map of Manhattan, you would still handle it as Euclidean plane with polygons, and disregard the curvature of the Earth.

However, if you need to locate the shortest distance for a plane to fly from NY to Chicago, you would have to take the curvature of the Earth into account, going the ellipsoid way as noted by your post.

Kalman Toth, SQL Server 2008 Training

http://www.sqlusa.com