Fce 552 part1

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


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).




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.



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”.


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.


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.


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.


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.


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.



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.


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.


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.


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.


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



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



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.



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.


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.


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.


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.

Fce 552 part1

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Fce 552 part1