AN EMPIRICAL METHOD FOR REFRACTION MODELLING IN TRIGONOMETRICAL HEIGHTING

Abstract

The monitoring of vertical displacements of engineering structures is largely carried out by spirit levelling. Sometimes spirit levelling may turn out to be not only slow and laborious, but also impractical. This is when trigonometrical levelling is considered. The Earth's curvature and atmospheric refraction effects are substantially eliminated by using simultaneous reciprocal levelling. However, there are situations when neither spirit levelling nor reciprocal trigonometrical levelling are appropriate. Targets on near vertical high dam walls can be observed from a number of control stations in a one-way trigonometrical mode, with no possibility of reciprocal observations. The same applies to tall buildings, chimneys and other inaccessible structures. Test observations made by using one-second theodolites and applying well known standard textbook models have consistently demonstrated that one-way trigonometrical levelling leads to accuracies ranging from 10 to 100 mm-per-kilometre, well below the requirements for monitoring the vertical displacements of structures.