Abstract
In classical two-dimensional (2D) geodetic networks, reducing slope distances to horizontal ones is an important task for engineers. These horizontal distances along with horizontal directions are used in 2D geodetic adjustment. The common practice for this reduction is the use of vertical angles to reduce distances using trigonometric rules. However, one faces systematic effects when using vertical angles. These effects are mainly due to refraction, deflection of the vertical (DOV), and the geometric effect of the reference surface (sphere or ellipsoid). To mitigate refraction and DOV effects, one can choose to observe the vertical angles reciprocally if the baseline points’ elevation difference is small. This paper quantifies these effects and proposes a proper solution to eliminate the effects in small-scale geodetic networks (where the longest distances are less than 5 km). The goal is to calculate slope distances into horizontal ones appropriately. For this purpose, we used the SWEN17_RH2000 quasigeoid model (in Sweden) to study the impact of the DOV applying different baseline lengths, azimuths, and vertical angles. Finally, we propose an approach to study the impact of the geometric effect on vertical angles. We illustrate that the DOV and the geometric effects on vertical angles measured reciprocally are significant if the height difference of the start point and endpoint in the baseline is large. Geometric correction should be considered for the measured vertical angles to calculate horizontal distances correctly if the network points are not on the same elevation, even if the vertical angles are measured reciprocally.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The available data are: (1) the deflection of vertical (DOV) components in Sweden and (2) MATLAB code for calculating the curvature-skewness problem.
Acknowledgments
The authors are grateful to Dr. Mahmoud Mohammad Karim from K. N. Toosi University of Technology (Iran), whose lectures inspired the main subject of this paper. We would like to thank the anonymous reviewers for taking the time, their careful reading of our manuscript, and their many insightful comments and suggestions.
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Published In
Journal of Surveying Engineering
Volume 149 • Issue 1 • February 2023
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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, https://creativecommons.org/licenses/by/4.0/.
History
Received: Jan 27, 2022
Accepted: May 31, 2022
Published online: Sep 26, 2022
Published in print: Feb 1, 2023
Discussion open until: Feb 26, 2023
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