Establishing and Maintaining a Cartesian Plane on a Geodetic Surface in Large Scale Industrial Metrology

Abstract

In 3D coordinate metrology the elevation reference is the plumb line, and the horizontal plane is normal to it – but engineering designs are modelled in rectangular Cartesian coordinates, and over hundreds of metres the earth stops cooperating. Laser trackers, precision levels and theodolites all level to their own local gravity vector, so as distance from the origin grows, the geopotential surface departs from the horizontal plane and the instrument's Z axis is no longer parallel to the Cartesian one. Across a control network of tens or hundreds of setups, the measured elevations follow the earth's geopotential surface rather than the designer's flat plane. Jansma and Banjanac set out the techniques for establishing and holding a flat Cartesian plane on a curved geodetic surface, and the earth-curvature corrections that accelerator alignment in particular demands.