Μέτρηση του υψομετρικού δικτύου της πολυτεχνειούπολης με τη μέθοδο της τριγωνομετρικής υψομετρίας ακριβείας (τρ.υ.α.)

Abstract

διπλωματική εργασία αποτελείται από πέντε κεφάλαια. Στο πρώτο κεφάλαιο γίνεται αναφορά στις υπάρχουσες μεθόδους μέτρησης ορθομετρικών υψομετρικών διαφορών. Περιγράφονται οι μέθοδοι της Γεωμετρικής Χωροστάθμησης, της Τριγωνομετρικής Υψομετρίας και της Ειδικής Τριγωνομετρίας Υψομετρίας και αναφέρονται τα μειονεκτήματα και τα πλεονεκτήματά τους. Στο δεύτερο κεφάλαιο γίνεται παρουσίαση και αναλυτική περιγραφή της Τριγωνομετρικής Υψομετρίας Ακριβείας (ΤΡ.Υ.Α.) και των εφαρμογών της. Επίσης, γίνεται ανάλυση των ακριβειών που μπορούν να επιτευχθούν με την ΤΡ.Υ.Α. καθώς και ανάλυση της επίδρασης των αβεβαιοτήτων των μεγεθών που υπεισέρχονται στον υπολογοσμό των υψομετρικών διαφορών. Στο τρίτο κεφάλαιο γίνεται περιγραφή της διαδικασίας μέτρησης του υψομετρικού δικτύου. Περιγράφεται με τη σειρά η αναγνώριση της περιοχής μελέτης, η επιλογή του εξοπλισμού, ο σχεδιασμός του δικτύου, οι μετρήσεις υπαίθρου και τα προβλήματα που προέκυψαν κατά τη διάρκειά τους. Στη συνέχεια γίνεται παρουσίαση των αποτελεσμάτων των μετρήσεων και στο τέλος παρουσιάζεται η συνόρθωση του δικτύου Στο τέταρτο κεφάλαιο γίνεται σύγκριση της ΤΡ.Υ.Α με την Ψηφιακή Γεωμετρική Χωροστάθμηση. Η σύγκριση αφορά στα αποτελέσματα που προέκυψαν από τη μέτρηση του ίδιου υψομετρικού δικτύου και με τις δύο μεθόδους. Έγινε σύγκριση των αποτελεσμάτων που προέκυψαν από τη διαδικασία της βελτιστοποίησης, πριν τη συνόρθωση, μετά τη συνόρθωση ενώ τέλος έγινε σύγκριση χρόνων. Στο πέμπτο και τελευταίο κεφάλαιο, συγκεντρώθηκαν όλα τα συμπεράσματα που προέκυψαν κατά την εφαρμογή της μεθόδου και την σύγκρισή της με την Ψηφιακή Γεωμετρική Χωροστάθμηση. Παρουσιάζονται και κάποιες προτάσεις που ίσως φανούν χρήσιμες στο μέλλον. Τέλος γίνεται αναφορά στον χρόνο που χρειάστηκε για την εκπόνηση της διπλωματικής εργασίας.

In this diploma thesis the method of the Accurate Trigonometric Heighting (A.T.H) is used for the accurate height difference determination between accessible or inaccessible points. The orthometric height difference is measured traditionally with the spirit leveling method. Recently, the use of digita1 levels provides significant improvements in the quickness and accuracy. Also, this determination may be done by the trigonometric heighting method for low accuracy works or by the specia1 trigonometric heighting method between benchmarks for high accuracy applications. The manufacture of the ref1ectorless tota1 stations gives the opportunity of direct distance measurements to inaccessible points. The measurements are carried out simultaneously and reciprocally between the instrument and the target positions in two directions (aller -retour). The application of the method is feasible by the use of modern reflectorless total stations. Initially, becomes description of the methods that are used in the current season for the determination of orthometric height differences. Then the methodology is described. The instrumentation needed and the theoretical analysis of the achieved precision is referred. The influence of the error of the measured values (distances and angles), of the change of the refraction coefficient κ and of the curvature of the earth in the final determined height difference value are analyzed. Useful remarks for the proper application of the methodology are stated. The planning, the measurement and the adjustment of the height network that exists in the campus of the National and Technical University of Athens are presented and analyzed. The results are compared with the results that had been extracted from the measurement of the same network with the digital leveling method in 2003. The conclusions deal with the advantages of the proposed method. Also, the best instrumentation combinations are mentioned in order to achieve the desired precision in any case. The single station of the method is presented in figure 2.1. It may be applied between accessible or inaccessible points in case that they are both visible from the total station position. The orthometric height difference between points Α and Β is calculated by the equations (2.1), (2.2) and (2.3). In the case that points Α and Β are not visible from the tota1 station position or the distance between them is long, the procedure that is described in figure 2.2 is applied. Α tripod bearing the tota1 station is put close to point Α. Another tripod bearing the target is put close to point Β. (2.2a). The tota1 station measures the distance DA and the zenith angle ΖΑ to point Α. Continually sights to the target and measures the distance D12 and the zenith angle Ζ12. Then the total station and the target change their positions reciprocally above the tribraches. Specia1 care is needed to avoid moving the tripod - tribrach system during the change. The tota1 station is put on the tripod Τ2, as the target is put on the tripod Τ1 (fig. 2.2b). The corresponding elements (D21, z21, DB, zΒ) are measured. The height difference ΔΗΑΒ between the points Α and Β is determined by the equation (2.4) where the height differences ΔΗA, ΔΗΒ, ΔΗ12 and ΔΗ21 are calculated according to the equations (2.2), (2.3), (2.5) and (2.6). If more stations are needed between points Α and Β, the three tripod method is applied (fig.2.3). In this case, the final height difference is calculated by the equation (2.7). The precision achieved by the proposed method is independent of: - The value of the geodetic refraction coefficient κ. - The curvature of the surface of the earth. - The measurement of the height of the instrument and target. Although it depends on: - The distance measurement precision. (Figure 2.8 illustrates the error of the height difference determination relative to the error in the distance measurement and the vertical angle value). - The zenith angle measurement precision. (Figures 2.9 and 2.10 illustrate the error of the height difference determination relative to the error in the vertical angle measurement (σz=±3cc and σΖ=±10cc) and the distance). - The change of the refraction coefficient κ during the measurements. (Figure 2.11 illustrates the error of the height difference determination relative to the change of the refraction coefficient κ (δκ=±0.05) during the measurements) . Under the presupposition that the measurements at each station in both directions were carried out simultaneously, (last short time), then there is not change in the refraction coefficient value. in this case, the final height difference is free of this error. Via the application of the variance-covariance low for one, two or more stations of the instruments the equations (2.17),(2.18),(2.19) calculate the final precision of the height difference determination between two points Α and Β by the A.T.H. CONCLUSIONS • The reflectorless total stations provide us with the capability of the direct determination of height differences between accessible or inaccessible points with adequate precision. • Βy the suggested method of the accurate trigonometric heighting (A.Τ.Η), the height difference between any points situated at special positions as gaps on the earth, high inclination surfaces, rough surfaces, structures, trigonometric network points, can be determined. • The method is quick, easy and convenient for application as the measurements are carried out simultaneously and reciprocally in both directions. Also, the tripods are put on casual positions without the need of centering. This improves the followed way. • The calculated height difference is free of: - The measurement of the height of the instrument and target. - The different manufactured height of the instrument and the target. - The geodetic refraction coefficient κ. - The curvature of the earth. • The provided by the total station precision for the zenith angle measurement is significant as it improves the final precision of the determined height difference. • For the measurement of the network using the method of digital leveling the number of stations needed are about four times more than by using the A.T.H. • The adjustment of the network has shown that the A.T.H. can achieve equal precision to the digital leveling method. • The errors of the closed polygons of a network are of high importance for the final determination of the uncertainties of the height of the network points and the measured height differences of the network. • In many application the use of the A.T.H. method provides the same precision to the digital leveling saving time.