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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
             Resection
B.Sc. (Civil Engineering)                                 University of Nairobi
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
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
FCE 552: Engineering Survey IV   Dept. of Geospatial & Space Technology



     Introduction to Horizontal Positioning-3




B.Sc. (Civil Engineering)                           University of Nairobi
FCE 552: Engineering Survey IV   Dept. of Geospatial & Space Technology



     Introduction to Horizontal Positioning-4




B.Sc. (Civil Engineering)                           University of Nairobi
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
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
FCE 552: Engineering Survey IV        Dept. of Geospatial & Space Technology



                            Datum Defects-2
Here angles P1, P2 and P3 have been precisely observed
using an appropriate theodolite.
Measurements of angles provide information about the
shape 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
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
FCE 552: Engineering Survey IV        Dept. of Geospatial & Space Technology



                            Datum Defects-4
For the above example, one can remove the defects as
follows:
Fix x and y coordinates of one point to control the
translation defects; or
Fix bearing of one line to prevent a rotation; or
Measure the length of at least one observation line within
the network to control scale.
Note that presence of datum defects depends on which
observations have been made for a particular network. For
example, a network whereby distances are measured will
not have a scale defect.
B.Sc. (Civil Engineering)                                University of Nairobi
FCE 552: Engineering Survey IV     Dept. of Geospatial & Space Technology



                Provision of Horizontal Control

One or more of the following methods have been used
in 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
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
FCE 552: Engineering Survey IV          Dept. of Geospatial & Space Technology


                              Triangulation-2
A triangulation network consists of a series
of interconnected triangles with the length
of at least one triangle being measured. This    base line
length is called the base line.
The angles of the triangles are precisely
measured using a theodolite. The angles
provide for the shape of the triangle. The
vertices of the triangle are known as
triangulation points (TP) or stations.
Since the solution of each triangle depends
on the length and azimuth of the preceding
triangle, errors tend to accumulate as the
                                              Fig. 3: A geodetic network
construction of the network progresses.
The errors in azimuth are controlled by use
of Laplace stations. The errors in scale are
controlled by measuring base lines at
appropriate intervals.
 B.Sc. (Civil Engineering)                                  University of Nairobi
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. are
referred.
   Before the advent of space-based positioning methods, e.g.,
Global Positioning Service (GPS), triangulation methods were
used for surveys of high accuracy and those covering large
areas (e.g. a country) and particularly when the terrain was
rugged.
   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 commonly
used in establishment of local networks requiring high accuracy,
e.g., deformation monitoring networks.
 B.Sc. (Civil Engineering)                                  University of Nairobi
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; or
iii) Third order (or Tertiary) triangulation.
      First order triangulation is the highest possible
grade of triangulation and serves as a framework of
control points to which Secondary triangulation points
are connected.
      Third order triangulation points may be connected
to Second or First order points.
    B.Sc. (Civil Engineering)                           University of Nairobi
FCE 552: Engineering Survey IV                         Dept. of Geospatial & Space Technology


          Measurement of Horizontal Angles-1
a) 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
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                  F
FACE LEFT        00 17 24           32 31 43       56 07 02        73 12 39         00 17 14
FACE RIGHT      180 17 31       212 31 49         236 07 08       253 12 44        180 17 20
MEAN             00 17 27.5         32 31 46       56 07 05        73 12 41.5       00 17 17
REDUCED          00 17 27.5         32 31 46       56 07 05        73 12 41.5       00 17 17
ADJUSTED                 +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 27.5


FACE LEFT        90 17 14       122 21 37         145 56 52       163 02 24         90 17 30
FACE RIGHT      270 17 00       302 21 22         325 56 40       343 02 10        270 17 06
MEAN             90 17 07       122 21 29.5       145 56 46       163 02 17         90 17 18
REDUCED          00 17 27.5         32 31 50       56 07 06.5      73 12 37.5       00 17 38.5
ADJUSTED                  -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 27.5
FINAL            00 17 28           32 31 48       56 07 06        73 12 39         00 17 28

   B.Sc. (Civil Engineering)                                              University of Nairobi
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
FCE 552: Engineering Survey IV   Dept. of Geospatial & Space Technology



      Preparation of A Triangulation Survey-2
Reconnaissance 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
FCE 552: Engineering Survey IV             Dept. of Geospatial & Space Technology


                                  Trilateration
   This gained prominence since the
advent of long-range EDMs.
   Trilateration is based on the                                    E
trigonometric proposition that if the
three sides of a triangle are known, the
three angles can be computed.
   If all the three sides of the triangle
DEF have been measured with
EDM the three angles can be computed
by cosine formula.                          D                                          F
   Directions of the lines and positions of
                                                        Fig. 4: Trilateration
the points in the triangle can then be
computed as in traverse and
triangulation.
 B.Sc. (Civil Engineering)                                     University of Nairobi
FCE 552: Engineering Survey IV            Dept. of Geospatial & Space Technology


                                   Intersection
   Frequently in a triangulation system an occasion
arises in which a point, whose position is to be
determined is not occupied (such as J).
   This point can be determined by measuring the
two angles G and H at the two ends of the known              J
line and estimating the third angle J.
   The angle J is called a concluded angle.
   The method of estimation is called
intersection.
   In practice, an intersection station such as J
is observed from three or more regular
triangulation points in the net.
   This provides the necessary checks on the G                           H
                                                    Fig. 5: Intersection
accuracy and reliability of the intersection
station.
  B.Sc. (Civil Engineering)                                    University of Nairobi
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 called
K                                    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

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Fce 552 part1

  • 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 Resection B.Sc. (Civil Engineering) University of Nairobi
  • 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. 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-3 B.Sc. (Civil Engineering) University of Nairobi
  • 5. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Introduction to Horizontal Positioning-4 B.Sc. (Civil Engineering) University of Nairobi
  • 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. 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-2 Here angles P1, P2 and P3 have been precisely observed using an appropriate theodolite. Measurements of angles provide information about the shape 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. 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Datum Defects-4 For the above example, one can remove the defects as follows: Fix x and y coordinates of one point to control the translation defects; or Fix bearing of one line to prevent a rotation; or Measure the length of at least one observation line within the network to control scale. Note that presence of datum defects depends on which observations have been made for a particular network. For example, a network whereby distances are measured will not have a scale defect. B.Sc. (Civil Engineering) University of Nairobi
  • 11. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Provision of Horizontal Control One or more of the following methods have been used in 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. 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Triangulation-2 A triangulation network consists of a series of interconnected triangles with the length of at least one triangle being measured. This base line length is called the base line. The angles of the triangles are precisely measured using a theodolite. The angles provide for the shape of the triangle. The vertices of the triangle are known as triangulation points (TP) or stations. Since the solution of each triangle depends on the length and azimuth of the preceding triangle, errors tend to accumulate as the Fig. 3: A geodetic network construction of the network progresses. The errors in azimuth are controlled by use of Laplace stations. The errors in scale are controlled by measuring base lines at appropriate intervals. B.Sc. (Civil Engineering) University of Nairobi
  • 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. are referred. Before the advent of space-based positioning methods, e.g., Global Positioning Service (GPS), triangulation methods were used for surveys of high accuracy and those covering large areas (e.g. a country) and particularly when the terrain was rugged. 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 commonly used in establishment of local networks requiring high accuracy, e.g., deformation monitoring networks. B.Sc. (Civil Engineering) University of Nairobi
  • 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; or iii) Third order (or Tertiary) triangulation. First order triangulation is the highest possible grade of triangulation and serves as a framework of control points to which Secondary triangulation points are connected. Third order triangulation points may be connected to Second or First order points. B.Sc. (Civil Engineering) University of Nairobi
  • 16. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Measurement of Horizontal Angles-1 a) 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. 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 F FACE LEFT 00 17 24 32 31 43 56 07 02 73 12 39 00 17 14 FACE RIGHT 180 17 31 212 31 49 236 07 08 253 12 44 180 17 20 MEAN 00 17 27.5 32 31 46 56 07 05 73 12 41.5 00 17 17 REDUCED 00 17 27.5 32 31 46 56 07 05 73 12 41.5 00 17 17 ADJUSTED +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 27.5 FACE LEFT 90 17 14 122 21 37 145 56 52 163 02 24 90 17 30 FACE RIGHT 270 17 00 302 21 22 325 56 40 343 02 10 270 17 06 MEAN 90 17 07 122 21 29.5 145 56 46 163 02 17 90 17 18 REDUCED 00 17 27.5 32 31 50 56 07 06.5 73 12 37.5 00 17 38.5 ADJUSTED -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 27.5 FINAL 00 17 28 32 31 48 56 07 06 73 12 39 00 17 28 B.Sc. (Civil Engineering) University of Nairobi
  • 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Preparation of A Triangulation Survey-2 Reconnaissance 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. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Trilateration This gained prominence since the advent of long-range EDMs. Trilateration is based on the E trigonometric proposition that if the three sides of a triangle are known, the three angles can be computed. If all the three sides of the triangle DEF have been measured with EDM the three angles can be computed by cosine formula. D F Directions of the lines and positions of Fig. 4: Trilateration the points in the triangle can then be computed as in traverse and triangulation. B.Sc. (Civil Engineering) University of Nairobi
  • 21. FCE 552: Engineering Survey IV Dept. of Geospatial & Space Technology Intersection Frequently in a triangulation system an occasion arises in which a point, whose position is to be determined is not occupied (such as J). This point can be determined by measuring the two angles G and H at the two ends of the known J line and estimating the third angle J. The angle J is called a concluded angle. The method of estimation is called intersection. In practice, an intersection station such as J is observed from three or more regular triangulation points in the net. This provides the necessary checks on the G H Fig. 5: Intersection accuracy and reliability of the intersection station. B.Sc. (Civil Engineering) University of Nairobi
  • 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 called K 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