Calculating the Position and Radius of the Center of a Curve Whose Horizontal Distance and Deflection Angle Are Measured From a Station in the Line of the Braces to the Circle Arc

Year 2021, Volume: 5 Issue: 2, 71 - 78, 22.12.2021

Hüseyin İnce Nuri Erdem Fazlı Engin Tombuş İbrahim Murat Ozulu

Abstract

In the production of the existing map, which is the basis for the construction of the zoning plans, and in the first facility cadastre, structures such as pools, buildings and minarets with a circle base are encountered. From a geodetic station point, it is possible to obtain the position and radius of the center of this structure whose base is circular with two consecutive beam lengths and polar measurements marked on such a structure. As a matter of fact, this issue has been seen in a study on the subject. In this study, the geodetic position of the center of the structure and the radius of the structure were tried to be obtained from a station point by using the horizontal angle between the tangent points of a structure with a circular base and the horizontal distance measured in the direction of the bisector of this angle. Since some publications of foreign origin do not enlighten the subject of research, it was deemed necessary to investigate the subject. In this study, first a theoretical explanation of the research subject was made, a numerical application was made on the subject and the findings and opinions obtained were stated.

Keywords

Radius Calculation,, Finding Circle Center Coordinate,, Polar Measurements

References

• [1]. İnce, H. And Erdem, N., (2020). ‘Investigation Of The Center Coordinates Of A Circle With Unknown Radius Using Polar Measurements’, International Journal Of Engineering And Geosciences (Ijeg), Vol; 4, Issue; 1, Pp. 026-032, February, 2020,
• [2]. Kåsa, I. (1976). A circle fitting procedure and its error analysis. IEEE Transactions on instrumentation and measurement, (1), pp.8-14.
• [3]. Coope, I. D. (1993). Circle fitting by linear and nonlinear least squares. Journal of Optimization Theory and Applications, 76(2), pp.381-388.
• [4]. Kavanagh, F. B., 2003, Geomatics, Pearson Education Inc.Prentice Hall, Upper Saddle River, NJ pp. 159–160.
• [5]. Kavanagh, F.B., 2009. Surveying Principles and Application. 8th ed. Columbus: Pearson Education Inc., pp.505
• [6]. Wolf, P. R., and Ghilani, C. D., 2008. Elementary Surveying an Introduction to Geomatics. 12th Edition, Upper Saddle River, New Jersey: Pearson Prentice-Hall. pp.271-274, 716-717, 720-721
• [7]. Cuomo, Paul A. (1997). Surveying Principles for Civil Enineers, Professional Publication İnc. 1250 Fifth Avenue, Belmost, CA 94002, Nited State Of America, pp.62
• [8]. Wolf, P. R., and Brinker R. C., 1989. Elementary Surveying, 8th Edition, Harper Collins Pulishers, pp.163-167.
• [9]. Bannister, A., Baker, R., and Raymond, S., 1992, Surveying, John Willey & Sons. Inc., New York, pp. 186–188.
• [10]. Bannister, A., Raymond, S. and Baker, R., 1998. Surveying. 7th ed. Harlow, UK: Addison Wesley Longman Limited Edinburg Gate, pp.81–82.
• [11]. URL 1: https://www.baytekin.com.tr/urun/kagit-ve-plastik-prizmalar/kagit-reflektor-6cm-x-6cm-gumus, Accessed date: 20.01.2021
• [12]. URL 2 : https://www.baytekin.com.tr/urun/prizma-takimlari/trimble-dairesel-reflektor-seti, Accessed date: 23.02.2021