Term of Award

Summer 2021

Degree Name

Master of Science, Civil Engineering

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


Department of Civil Engineering and Construction

Committee Chair

Gustavo Maldonado

Committee Member 1

Marcel Maghiar

Committee Member 2

Francisco Cubas-Suazo


This study presents two novel approaches to balance the horizontal longitudinal error of closure, EC, in closed polygonal traverses. The standard procedure to balance EC is the Compass Rule. This technique reduces EC to zero by applying corrections in the lengths of all traverse sides. Those corrections are proportional to the corresponding side lengths. That is, this approach is not an error-correcting approach, but an error-balancing procedure.

The proposed new techniques are based on sensitivity analysis of EC with respect to small variations, Δi, in the lengths of all sides i = 1, 2, …, n of the traverse, where n is the total number of sides. In fact, for improved visualization purposes, the sensitivity analysis is performed on quantity D = P/EC, where P is the perimeter of the traverse. Additionally, D is the denominator of the Longitudinal Precision Ratio, LPR = 1/D, of the traverse.

The presented new schemes first select the side lengths to be modified as those showing the most pronounced variations in D. Then, after the length of a few selected sides are modified, the Compass Rule is applied to close the remaining small gap. One of the proposed schemes requires a single sensitivity analysis and modifies the length of a few sides simultaneously, whereas the other scheme requires iterative sensitivity analyses and modifies the length of only one side per iteration.

Potential weaknesses of the proposed schemes were investigated and analyzed. Additionally, an attempt was made to corroborate if the proposed schemes were truly error-correcting approaches or just error-balancing ones. However, the attempt was inconclusive due to unexpected inaccuracies in a few side lengths employed as benchmarks. Those lengths were obtained from vertex coordinates acquired by Leica GS14 antennas. Unfortunately, 2 vertices out of 7 presented quality-control parameters slightly out of the suggested preferred ranges. Therefore, it could not be concluded that the proposed schemes are truly error-correcting ones. Nevertheless, they effectively reduce and fully eliminate the horizontal longitudinal error of closure in closed polygonal traverses. This corroborates that they are, at least, new effective error-balancing procedures.

Research Data and Supplementary Material