Adjustment Methods for Planimetric Observations and Co-Ordinates in Survey Networks

Sabbah, Abdel-Latif M. E (1967) Adjustment Methods for Planimetric Observations and Co-Ordinates in Survey Networks. PhD thesis, University of Glasgow.

Abstract

Correction and adjustment of observed angles and sides in geodetic networks are necessary for the purpose of the correct location of coordinated points. Correction equations are usually in the form of linear overdetermined (observation) or underdetermined (condition) equations which are solved by the least squares theorem. The introduction of the electro-magnetic methods of linear measurement requires the adjustment of sides as well as the adjustment of angles necessary in classical triangulation nets. For the simultaneous adjustment of angles and sides two new sets of conditions have been introduced: (i) the area misfit condition, where the area obtained from distances and angles has to satisfy a special condition, and (ii) that the sum of the projections of the three sides of a triangle on the coordinate axes have to satisfy a zero condition. A special study has been made into the adjustment of the braced geodetic quadrilateral, as being one of the most favourable figures from the adjustment point of view. The different apices of this quadrilateral have been investigated to allow a choice to be made as to which of them shall be introduced in an angle misfit condition during adjustment. This gives rise to the conclusion that all apices will introduce the same corrections for all practical purposes. Since observed angles and sides are different physical quantities, the question of relative weighting has been given special attention and recommendations have been made in the light of various theoretical and practical investigations. The Systematic relaxation method for adjusting survey nets has been theoretically derived by Professors Southwell and Black based on the minimum strain-energy conserved in an elastic frame-work at the position of equilibrium. Using this theory mechanical analogues have been designed and constructed for the first time to carry out the adjustment of the triangulation net directly from field observations, without the necessity of forming and solving a set of linear equations. An analogue for the adjustment of angles was found to be excessively complicated mechanically and difficult to use in practice. Through the use of a direction adjustment method these limitations have been overcome. The final model constructed achieved comparable results to those obtained numerically by a least squares solution. Suggestions for a more highly developed version are made and the situations favourable to mechanical analogue computations are discussed. The use of an electrical analogue as suggested by Su using a D.C. circuit has been thoroughly investigated from both the theoretical and practical points of view, which showed that such a solution will be simple only for certain limited cases. As an alternative the possibilities of the more general purpose electronic analogue computer have been investigated via the solution of correction equations. Various examples have been solved on this computer which proved to have several advantages over other computation methods. Finally equivalent problems have been solved numerically on a digital computer for a comparison of the relative merits of analogue and digital methods for the particular case of adjustment of geodetic networks. The relative merits of these solutions are discussed in the light of different problems and circumstances.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Remote sensing, Geographic information science and geodesy
• Date of Award: 1967
• Depositing User: Enlighten Team
• Unique ID: glathesis:1967-78435
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 30 Jan 2020 15:27
• Last Modified: 30 Jan 2020 15:27
• URI: https://theses.gla.ac.uk/id/eprint/78435