Discrepancies between planar and geodesic distances as a function of azimuthal variability

Plane surveying measurements usually adopt a topocentric system, suitable for small areas, which can be either a Local Astronomic System - LAS, referenced to the geoid, or a Local Geodetic System - LGS, referenced to the ellipsoid. In modern geodetic measurements, however, a geocentric reference system associated with the ellipsoid is commonly used. Since topocentric systems differ only in the orientation of their axes, the reduction to the ellipsoid and the use of the LGS are important for reconciling field observations and geodetic computations. Nevertheless, planar distances in the LGS do not follow the ellipsoidal surface, requiring conversion. As the radii of the normal sections on the ellipsoid vary with the azimuth, it is hypothesized that the conversion values may also vary. To test this hypothesis, a planar distance of ten thousand meters was used in different azimuths in the LGS with origin at the RSCL station, in the Municipality of Cerro Largo, State of Rio Grande do Sul, Brazil. The resulting differences were on the order of 10⁻⁵ meters, that, depending on the project objectives, they may be relevant.