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# Fce 552 part1

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### Fce 552 part1

1. 1. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Outline 1) Introduction to Horizontal Positioning 2) Datum Defects 3) Provision of Horizontal Control Triangulation Trilateration Intersection ResectionB.Sc. (Civil Engineering) University of Nairobi
2. 2. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-1 Surveying (or geodesy) covers the determination of horizontal and vertical positions as well as the gravity intensity of points on the earth’s surface. Need to differentiate between vertical or height measurements (1D); horizontal or planimetric measurements (2D); combined horizontal and vertical measurements (3D) and combined horizontal, vertical and time measurements (4D).B.Sc. (Civil Engineering) University of Nairobi
3. 3. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-2 The separation of the two components of positioning i.e., vertical and horizontal was due to the fact that different instruments were used for determination of each component. Furthermore, the reference surfaces used for each component are different. Technological developments have led to more precise instrumentation and improved models for computations leading to modern three- and four- dimensional networks.B.Sc. (Civil Engineering) University of Nairobi
4. 4. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-3B.Sc. (Civil Engineering) University of Nairobi
5. 5. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-4B.Sc. (Civil Engineering) University of Nairobi
6. 6. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-5 In carrying out the measurements, we respect the three principles, namely:1. Working from “whole to the part”;2. Reliability control (independent checks to both measurements and processing (computations) are needed and use of tested computer programs is made;3. Economy: cost considerations are important. “Be accurate as possible, but not more than required”.B.Sc. (Civil Engineering) University of Nairobi
7. 7. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-1 For provision of horizontal control for a large area P2 e.g., a country, the Earth’s surface is covered by a network of points that are arranged in such a way that neighboring points build a triangle. Consider a horizontal survey network consisting P1 P3 of three points as shown Fig. 1: Datum defects in Fig. 1.B.Sc. (Civil Engineering) University of Nairobi
8. 8. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-2Here angles P1, P2 and P3 have been precisely observedusing an appropriate theodolite.Measurements of angles provide information about theshape of the network.If none of the points is known in position (i.e., x, y),then the following can happen to the 2-D network: translate in x – direction; translate in y- direction; rotate about a vertical axis; take any size.B.Sc. (Civil Engineering) University of Nairobi
9. 9. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-3 In the above case, we say that the network has four free datum parameters or datum defects, namely 2 translation (one in x-axis and the other in y-axis), one rotation and a scale. It is normally not possible to compute the position of points if there are datum defects present in the network. One is required to remove these defects. The presence of defects is because most surveying observations do not provide information concerning the coordinate system e.g., the coordinate system origin, while the computation models have the coordinates as parameters.B.Sc. (Civil Engineering) University of Nairobi
10. 10. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-4For the above example, one can remove the defects asfollows:Fix x and y coordinates of one point to control thetranslation defects; orFix bearing of one line to prevent a rotation; orMeasure the length of at least one observation line withinthe network to control scale.Note that presence of datum defects depends on whichobservations have been made for a particular network. Forexample, a network whereby distances are measured willnot have a scale defect.B.Sc. (Civil Engineering) University of Nairobi
11. 11. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Provision of Horizontal ControlOne or more of the following methods have been usedin the provision of horizontal control: Triangulation; Traversing; Trilateration; Space techniques using Global Navigation Satellite System (GNSS) e.g., GPS, GLONASS, GALILEO; Inertial Surveying.B.Sc. (Civil Engineering) University of Nairobi
12. 12. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Triangulation-1 Triangulation originates from the Latin word tres angulus (tres = three; angulus = angle). P2 It is a method of surveying in which the position of a new point is determined from the mathematical solution of the triangle whose vertices are the new point and the two other points of known position. Fig. 2 shows survey points P1 P1 P3 and P2 as known (known Fig. 2: Triangulation net coordinates) points while P3 is a new point whose coordinates are desired.B.Sc. (Civil Engineering) University of Nairobi
13. 13. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Triangulation-2A triangulation network consists of a seriesof interconnected triangles with the lengthof at least one triangle being measured. This base linelength is called the base line.The angles of the triangles are preciselymeasured using a theodolite. The anglesprovide for the shape of the triangle. Thevertices of the triangle are known astriangulation points (TP) or stations.Since the solution of each triangle dependson the length and azimuth of the precedingtriangle, errors tend to accumulate as the Fig. 3: A geodetic networkconstruction of the network progresses.The errors in azimuth are controlled by useof Laplace stations. The errors in scale arecontrolled by measuring base lines atappropriate intervals. B.Sc. (Civil Engineering) University of Nairobi
14. 14. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Triangulation-3 The resulting system of horizontal control (point coordinates)from triangulation serves as a framework to which cadastral,topographical, engineering, hydrographical, GIS maps etc. arereferred. Before the advent of space-based positioning methods, e.g.,Global Positioning Service (GPS), triangulation methods wereused for surveys of high accuracy and those covering largeareas (e.g. a country) and particularly when the terrain wasrugged. In Kenya, the main existing horizontal control framework(surveys) were carried out by means of triangulation. Apart from using triangulation for nationwide surveys,triangulation combined with distance measurements, is commonlyused in establishment of local networks requiring high accuracy,e.g., deformation monitoring networks. B.Sc. (Civil Engineering) University of Nairobi
15. 15. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Classification of Triangulation Surveys Triangulation surveys are graded as :i) First order (or Primary) triangulation;ii) Second order (or Secondary) triangulation; oriii) Third order (or Tertiary) triangulation. First order triangulation is the highest possiblegrade of triangulation and serves as a framework ofcontrol points to which Secondary triangulation pointsare connected. Third order triangulation points may be connectedto Second or First order points. B.Sc. (Civil Engineering) University of Nairobi
16. 16. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Measurement of Horizontal Angles-1a) Direction Method (with Round open) TABLE 1: OBSERVATIONS WITH THE ROUND OPEN F (RO) G C B FACE LEFT 00 17 24 32 31 43 56 07 02 73 12 39 FACE RIGHT 180 17 31 212 31 49 236 07 08 253 12 44 MEAN 00 17 27.5 32 31 46 56 07 05 73 12 41.5 REDUCED 00 17 27.5 32 31 46 56 07 05 73 12 41.5 FACE LEFT 90 07 14 122 21 37 145 56 52 163 02 24 FACE RIGHT 270 07 00 302 21 22 325 56 40 343 02 10 MEAN 90 07 07 122 21 29.5 145 56 46 163 02 17 REDUCED 00 17 27.5 32 31 50 56 07 06.5 73 12 37.5 FINAL 00 17 28 32 31 48 56 07 06 73 12 40 B.Sc. (Civil Engineering) University of Nairobi
17. 17. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Measurement of Horizontal Angles-2 b) Direction Method (with Round closed) TABLE 2: OBSERVATIONS WITH THE ROUND CLOSED F (RO) G C B FFACE LEFT 00 17 24 32 31 43 56 07 02 73 12 39 00 17 14FACE RIGHT 180 17 31 212 31 49 236 07 08 253 12 44 180 17 20MEAN 00 17 27.5 32 31 46 56 07 05 73 12 41.5 00 17 17REDUCED 00 17 27.5 32 31 46 56 07 05 73 12 41.5 00 17 17ADJUSTED +0 +2.6 +5.3 +7.9 +10.5 00 17 27.5 32 31 48.6 56 07 10.3 73 12 49.4 00 17 27.5FACE LEFT 90 17 14 122 21 37 145 56 52 163 02 24 90 17 30FACE RIGHT 270 17 00 302 21 22 325 56 40 343 02 10 270 17 06MEAN 90 17 07 122 21 29.5 145 56 46 163 02 17 90 17 18REDUCED 00 17 27.5 32 31 50 56 07 06.5 73 12 37.5 00 17 38.5ADJUSTED -0 -2.8 -5.5 -8.3 -11 00 17 27.5 32 31 47.5 56 07 01 73 12 29.2 00 17 27.5FINAL 00 17 28 32 31 48 56 07 06 73 12 39 00 17 28 B.Sc. (Civil Engineering) University of Nairobi
18. 18. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Preparation of A Triangulation Survey-1 This consists of the following: recconaissance (recce.) erection of signals or station marks measurement of base lines measurement of horizontal angles establishment of Laplace stations data processing or computations.B.Sc. (Civil Engineering) University of Nairobi
19. 19. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Preparation of A Triangulation Survey-2Reconnaissance involves: examination of the country to be surveyed selection of suitable sites for base lines selection of suitable positions for constructing TP’s confirmation of inter-visibility between stations ensuring that well conditioned triangles are chosen other factors, e.g., water and communication services. Use of existing maps is essential in reconnaissance surveys. B.Sc. (Civil Engineering) University of Nairobi
20. 20. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Trilateration This gained prominence since theadvent of long-range EDMs. Trilateration is based on the Etrigonometric proposition that if thethree sides of a triangle are known, thethree angles can be computed. If all the three sides of the triangleDEF have been measured withEDM the three angles can be computedby cosine formula. D F Directions of the lines and positions of Fig. 4: Trilaterationthe points in the triangle can then becomputed as in traverse andtriangulation. B.Sc. (Civil Engineering) University of Nairobi
21. 21. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Intersection Frequently in a triangulation system an occasionarises in which a point, whose position is to bedetermined is not occupied (such as J). This point can be determined by measuring thetwo angles G and H at the two ends of the known Jline and estimating the third angle J. The angle J is called a concluded angle. The method of estimation is calledintersection. In practice, an intersection station such as Jis observed from three or more regulartriangulation points in the net. This provides the necessary checks on the G H Fig. 5: Intersectionaccuracy and reliability of the intersectionstation. B.Sc. (Civil Engineering) University of Nairobi
22. 22. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Resection The method of locating a point P from at least three known points K, L, and M without M having occupied the known points is calledK resection. L In this system only the point to be determined is occupied, and the angles between the known stations are measured. A minimum of three known points is required to determine the position of the unknown point. In order to be able to resect P it is geometrically important that the known points P K,L and M don’t lie on the circumference of a Fig. 6: Resection circle, otherwise the danger circle situation results with no unique position for P being obtained. B.Sc. (Civil Engineering) University of Nairobi