Research on length deformation control of high-altitude linear engineering based on the ellipsoid expansion method

In engineering control surveys, the problem of length distortion arising from the reduction of field-measured distances to the Gauss plane has long posed challenges in practical applications, particularly in high-altitude linear engineering projects where such distortions are more pronounced. Effective methods for controlling this distortion remain unclear. This paper systematically analyzes the deformation patterns of ground survey distances reduced to the ellipsoid and then projected onto the Gauss plane. It also evaluates and compares the effectiveness of four ellipsoid expansion methods-mean curvature radius method, prime vertical curvature radius method, planar analytical method, and generalized differential calculus method-in establishing engineering ellipsoids for distortion control. The results demonstrate that the engineering ellipsoid constructed via the generalized differential calculus method achieves optimal control over length distortion, with a maximum distortion of only 11.4 mm, well below the specified tolerance limit (± 37.9 mm). The findings confirm that this method provides a reliable technical basis for establishing coordinate systems in linear engineering projects located in high-altitude regions.