Was it the curvature of the coordinate system you were using during machine install, or was it the actual curvature of earth's surface that was important here?
The actual curvature of the earth is what mattered. We used both laser interferometers and highly precise levels as part of the install.
If you assume the vertical axis and gravity are aligned, over the distances our machines moved the deviation between the two is enough to matter when setting up the machine alignment. The measurements would only match if you accounted for the curvature of the earth.
> If you assume the vertical axis and gravity are aligned
Gravity's vector is not the same as earth's surface-normal though - if you stand at the base of Mt. Everest then gravity is slightly angled compared to the curvature of the earth at that point.
There isn't really a local good reference for "earth's surface normal" at the scale we're talking here anyway, though - it seems that what matters is the divergence between the gravity vector at one end of the factory and the other.
If you assume the vertical axis and gravity are aligned, over the distances our machines moved the deviation between the two is enough to matter when setting up the machine alignment. The measurements would only match if you accounted for the curvature of the earth.