LAUSR

Abstract This article presents a new, original approach to modeling vertical refraction in trigonometric levelling. So-called polynomial transition curves are used here. In this approach, it is assumed that the refraction curve coincides with the polynomial transition curve. As a result, the refraction curve is strictly mathematically defined, which greatly simplifies any calculations that come into play in the trigonometric levelling. The proposed approach was verified on the basis of measurements of vertical displacements using the trigonometric leveling method at short distances. Appropriately marked target boards were used in the measurements. The point measured on each of the target boards was marked twice, i.e. it had a given initial position and a second position treated as the current position, shifted vertically by a given displacement value. Additionally, a third point was marked in the vertical line of each measuring board, which is used to correct the measured vertical angles in accordance with the proposed procedure. The results of the calculations showed that the proposed approach allows to significantly increase the accuracy of determining vertical displacements. As a result, the proposed approach to modeling vertical refraction with the use of polynomial transition curves can be assessed as useful in a measurement practice.