COMPARATIVE
STUDY OF STRENGTH OF FIGURE OF FOUR
BRACED QUADRILATERAL USING A MINOR TRIANGULATION SCHEME
DEPARTMENT: SURVEYING
& GEOINFORMATICS
CHAPTER
ONE
1.0
INTRODUCTION
1.1 Background of study
Triangulation
is one of the methods of fixing accurate controls on the earth surface. It is
based on the trigonometric proposition that if one side and two angles of a
triangle are known, the remaining sides can be computed. A triangulation system
consists of a series of overlapping triangles in which an occasional side
called a baseline is measured and remaining sides are calculated from the
angles measured at the vertices of the triangles, vertices being the control
points are called triangulation stations (Chandra, 2012).
See fig. 1.0 below
When
all sides of a triangulation are measured it is known as the triliteration
system.
However,
the angular measurement define the shape of the triangulation system better
than wholly linear measurements and so it is preferred that a number of angles
are included in trilateration system.
A
combined triangulation and trilateration system in which all the angles and all
the sides are measured, represents the strongest network for creating
horizontal control and it is called
triangulation.
Because,
at one time, it was easier to measure angles than it was for distance,
triangulation was the preferred method of establishing the position of control
points.
Many
countries used triangulation as the basis of their national mapping system. The
procedure was generally to establish primary triangulation networks, with
triangles having sides ranging from 30 to 50 km in length. The primary
trigonometric points were fixed at the corners of these triangles and the sum
of the measured angles was correct to ± 3″. These points were usually
established on the tops of mountains to afford long, uninterrupted sight lines.
The
process of measuring the angles of a chain network of triangles of the earth is
called triangulation. (Agor, 2010).
1.1.1 Objective of triangulation surveys
The
main objective of any triangulation or trilateration surveys is to provide a
number of stations whose relative and absolute positions, horizontal as well as
vertical, are accurately established. More detailed location or engineering
survey is then carried out from these stations.
The
triangulation surveys therefore are carried out for the following reasons:
(i)
To create accurate
control for plane and geodetic surveys of large areas, by terrestrial methods,
(ii)
To establish precise
control for photogrammetric surveys of large areas,
(iii)
To support in the determination of the size
and shape of the earth by making observations for latitude, longitude and
gravity, and
(iv) To determine accurate locations of points in
engineering works such as:
(a) Fitting centre line and abutments of long
bridges over large rivers.
(b) Fitting centre line, terminal points, and shafts
for extended tunnels.
(c) Transferring the control points across wide sea
channels, large water bodies, etc.
(d) Detection of crustal activities, etc.
(e) Finding the direction of the movement of clouds.
1.1.2
Strength of Figures
The
strength of figure is a thing to be considered in establishing a triangulation
system to maintain the computations within a desired degree of precision. It
plays also an important role in deciding the layout of triangulation system.
The strength of figure is a function of:
Angles
change more rapidly than those of large angles. This suggests that smaller
angles less than 30° should not be used in the computation of triangulation.
If, due to unavoidable circumstances, angles less than 30° are used, then it
must be ensured that this is not opposite the side whose length is required to
be computed for carrying forward the triangulation series.
The
expression given by the U.S coast and Geodetic survey for evaluation of
strength of figure is:
L2=
d2R
Where,
L2= the square of the probable
error that would occur in the sixth place of the logarithm of any side.
d=
the probable error of an observed direction in seconds of arc,
R=
a term which represents the shape of a figure
R = )
D= the number of directions observed
excluding the known side of the figure,
= the difference in the sixth place
of logarithm of the sine of the distance angles A, B, C, etc respectively,
C= (nˈ-Sˈ+1) + (n-2S+3)
nˈ= the total number of sides
including the known side of the figure,
n=the total number of sides observed
in both directions including the known side,
Sˈ= the number of stations occupied,
and
S= the total number of stations.
1.2
STATEMENT OF THE PROBLEM
It has been established that
the disregard for the consideration of strength of figure and also the absence
of the use of four braced quadrilateral figure in triangulation work are the
major factors resulting in in-accurate relative position fixing of control
points which is the basis for all survey work.
Since accuracy is a function of the strength of figure and four
quadrilateral figures in a triangulation scheme, there is need to evaluate and
consider a figure at the reconnaissance stage before triangulation. This is to
ensure high accuracy of fixation of points.
1.3
MOTIVATION OF RESEARCH
This project is carried out
due the degree of accuracy that will be required in minor triangulation scheme
of four braced quadrilateral
1.4
AIM OF THE
STUDY
The plan of this project is
to evaluate and examine the strength of figure of four braced quadrilateral
using a minor braced triangulation scheme.
1.5
OBJECTIVES OF THE STUDY
This aim will be achieved
through the following objectives:
- To observe internal angles of the braced quadrilateral
- To deduce the angles from the coordinates obtained.
- To determine the strength of figure of each braced quadrilateral
that is to be considered. - To compare results obtained from each figure of the four braced figure
for minor triangulation scheme. - To determine the best angles in the triangle.
1.6
STUDY AREA
The area of study is located in part of federal
university of technology, Minna; permanent campus Gidan-Kwano, it is located at
new bus park. The major socio-economic activities of the study area is farming.
It is located in Bosso local Government Area of Niger state. It lies on
longitude 6o27’08.’’4E and Latitude 9o32’03’’46N and
about 216.70m above Mean Sea Level.