fce 552 part1

Outline

Dept. of Geospatial & Space Technology

University of NairobiB.Sc. (Civil Engineering)

FCE 552: Engineering Survey IV

1) Introduction to Horizontal Positioning

2) Datum Defects

3) Provision of Horizontal Control

Triangulation

Trilateration

Intersection

Resection

Introduction to Horizontal Positioning-1Surveying (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).




Introduction to Horizontal Positioning-2The 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.







Introduction to Horizontal Positioning-3

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”.





For provision of horizontal control for a large area 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 of three points as shown in Fig. 1.

Datum Defects-1


University of Nairobi

P1

P2

P3

Fig. 1: Datum defects

B.Sc. (Civil Engineering)


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.




Datum Defects-2

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.




Datum Defects-3

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.




Datum Defects-4

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.

Provision of Horizontal Control




Triangulation originates from the Latin word tres angulus (tres = three; angulus = angle). 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 and P2 as known (known

coordinates) points while P3 is a new point whose

coordinates are desired.

Triangulation-1



P3P1

P2

Fig. 2: Triangulation net



A triangulation network consists of a series of interconnected triangles with the length of at least one triangle being measured. This 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 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.



Fig. 3: A geodetic network

base line



Triangulation-2



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.



Triangulation-3



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.

Classification of Triangulation Surveys





Measurement of Horizontal Angles-1

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

a) Direction Method (with Round open)

TABLE 1: OBSERVATIONS WITH THE ROUND OPEN





Measurement of Horizontal Angles-2b) Direction Method (with 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 00 17 27.5

+2.6 32 31 48.6

+5.3 56 07 10.3

+7.9 73 12 49.4

+10.5 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 00 17 27.5

-2.8 32 31 47.5

-5.5 56 07 01

-8.3 73 12 29.2

-11 00 17 27.5

FINAL 00 17 28 32 31 48 56 07 06 73 12 39 00 17 28

TABLE 2: OBSERVATIONS WITH THE ROUND CLOSED





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.

Preparation of A Triangulation Survey-1





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.

Preparation of A Triangulation Survey-2





This gained prominence since the advent of long-range EDMs.

Trilateration is based on the trigonometric proposition that if thethree 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.

Directions of the lines and positions of the points in the triangle can then be computed as in traverse and triangulation.

Trilateration

D F

E

Fig. 4: Trilateration





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 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 accuracy and reliability of the intersection station.

Intersection

Fig. 5: Intersection

J

G H





The method of locating a point P from at least three known points K, L, and M without having occupied the known points is called resection.

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 K,L and M don’t lie on the circumference of a circle, otherwise the danger circle situation results with no unique position for P being obtained.

Resection

Fig. 6: Resection

P

M

LK



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