At the end of this lecture student

should know;

 The purpose of control survey

 Methods in control survey
 Open, close traverse and its calculations
 Triangulation, trilateration and triangulateration

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 CONTROL SURVEY
Definitions

Control survey is the survey that provides a framework of

survey points, whose relative positions, in two or three
dimensions. The area covered by these points may be
extend over the whole country for mapping and may be
relative small e.g. the construction sites. Control surveys
can be divided into two, horizontal control for planimetric
positions x and y coordinates and vertical control for
different in level z coordinate.

Engineering Survey – ECG422

 Purposes of control survey

 Control networks provide a reference framework of

points for;
i. Topographic mapping and for large scale plan production
ii. Dimensional control y, x, z for any construction work
iii. Deformation monitoring survey for all manner of
structures both new and old
iv. Extension and densification of existing control networks

Engineering Survey – ECG422

 Methods used for control
surveys

 Triangulation
This is the early method, all angles measured plus one distance
 Trilateration
All distances measured
 Triangulateration a combination of triangulation and trilateration
All angles and all distances measured
 Traversing
Bearing or angle and distance for each line measured
 Satellite position fixing e.g. GPS and DGPS
Signal received processed to determine x,y,z coordinates in the
form of WGS84

Engineering Survey – ECG422

 TRAVERSING

 Traverse is the most popular method of establishing

control networks not only in engineering but also in
geodetic surveying. This is because of the flexibility of
the method. Station can be establish anywhere and can
be set direct to the project to be done. Instrument used
normally theodolite to observe bearing or angles and
EDM to measure distance between points. Nowadays
with the invention of total station instrument, by one
instrument we can measure distance and observe
angles straight forward; traverse become more easy to
carry out and more productive.

Engineering Survey – ECG422

 BASIC TRAVERSE METHOD
A

Distance BC

 Two parameters in traverse surveys are the angles or

bearing between two points and distance. In figure below,
AB is the base line, C can be determine it’s position by
measure distance BC and also angle ABC.

Engineering Survey – ECG422

 Types of Traverse

 Closed traverse
Means the survey for example start from A B
point A whether known or unknown and A
then close back at A, this type of traverse
called polygonal shape. If start from
known point A and then close to another Link Shape
known point B is called close traverse link Polygonal Shape
shape. One of the advantage of close
traverse is that we can determine the
error of the traverse.

 Open traverse
Means the survey start from A and then
didn’t close. The disadvantage of this A
traverse, we cannot check the error.
Open traverse

Engineering Survey – ECG422

 The Purposes of Traverse Survey

 To determine the position of the existing of boundary mark.

 To establish the position of boundary lines.
 To determine the area encompassed within the confines
boundaries.
 To determine the positions of arbitrary control points for mapping.
 To determine ground control for photogrammetric mapping.
 To establish ground control for detail surveys.
 To establish control points for setting out.

Engineering Survey – ECG422

 Error in Traverse Survey

 Angular Error
Error in the observation of horizontal and vertical angles.
 Linear Error
Error in the measurement of distance.
 Centering Error
Error in bisecting the cross hair of the telescope or plummet to
the object image, error related to parallax.

Three types of error in surveying, systematic, mistakes and

random error. Normally the remaining error in traverse is
random error, these can be reduced by using precise instrument
and three tripods system (TTS).
Engineering Survey – ECG422
 Traverse Computation
 Compute the latitudes and departures
 Compute the linear error or closure
 Compute the linear accuracy ratio of the survey. If the accuracy
ratio is unsatisfactory, complete the following steps;
 a. double check all computations.
 b. double check all data entries.
 c. compute the bearing of the linear error of closure and check if it is
similar to one of the course bearing +-5
 d. re-measure the sides of the traverse, beginning with the course
having a bearing similar to the bearing of the linear error of closure if
there is one.
 e. when a mistake or error is found, try the corrected value in the
traverse computation to determine the new accuracy ratio.

Engineering Survey – ECG422

 Example: Traverse Computation
Stn Bearing Distance Latitude Corr- Corr.Lat Departure Corr- Corr.Dep Northing Easting
1 100.000 100.000
2 87 42 30 181.131 7.243 -0.004 7.239 180.986 -0.012 180.974 107.239 280.974
3 178 39 0 115.902 -115.870 -0.003 -115.873 2.731 -0.008 2.723 -8.634 283.697
4 178 39 0 113.023 -112.992 -0.003 -112.994 2.663 -0.007 2.655 -121.628 286.352
5 269 25 0 181.234 -1.845 -0.004 -1.849 -181.225 -0.012 -181.237 -123.478 105.116
6 358 43 0 60.875 60.860 -0.001 60.858 -1.363 -0.004 -1.367 -62.619 103.749
1 358 41 0 162.666 162.623 -0.004 162.619 -3.738 -0.011 -3.749 100.000 100.000
814.831 0.019 -0.019 0.000 0.054 -0.054 0.000

Linear misclosure: 1 in 14,283

Area: 4.098 Ha

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 Exercise in class

Stn Bearing Distance

1
2 92 35 30 230.711
3 179 57 0 51.152
4 179 56 30 137.143
5 266 16 0 189.414
6 348 50 0 98.155
1 348 49 30 116.996

Engineering Survey – ECG422

Steps using Casio FX570W/MS,350TL/MS

P to R
Shift Rec, dist, ¸ , bearing , ) = get latitude
STO , (-), RCL, (-), ALPHA, tan = get departure

R to P

Shift Polc , Lat, ¸ , Dep, ) = get distance

STO, (-), RCL, (-), ALPHA, tan = get bearing

Engineering Survey – ECG422

 What we can obtain from traverse computation

 Determine the error amount for angular mis-closure.

 Determine linear accuracy ratio or survey precision.
 Compute the corrected bearing and distances after applying the
adjustment.
 Compute the coordinate of every station in the traverse.
 Compute the area of the polygonal traverse.

Engineering Survey – ECG422

Triangulation

 Triangulation is a form of horizontal control survey

applied when a very large area is to be surveyed and
where the method of traversing would not be
expected to maintain a uniformity high accuracy over
the entire area.
 Because at one time, it was easier to measure or to
observe angle than it was distance, so triangulation
was the preferred method of establishing the position
of control points.
 Many countries used triangulation as the basis for
control of their national mapping system.
 With the advent of EDM or total station instruments
and satellite positioning, now triangulation method is
obsolete.

Engineering Survey – ECG422

 Basic principle of
triangulation

 If the length of one side of a triangle is known and

any two triangles are measured then the length of the
other two sides can be calculated.
 The relative positions of the three points forming the
triangle can thus be established.
 The basic principle is adopted in triangulation survey,
where a series of connected triangles forming a
network is laid out over the ground, all the angles are
measured.
 Once the length of one side of one triangle in the
network is known, all other lengths can be calculated.
From these data the relative positions of all points
can be coordinated and plotted

Engineering Survey – ECG422

 Classes of triangulation
 Primary Triangulation(1st Order)
-Sides ranging from 31 - 50 km, well condition
triangle, angle read to 0.2” or less, standard error
between 1 : 50000 to 1 : 100000
 Secondary Triangulation(2nd Order)
-Sides ranging from 16 - 30 km, angle read to 1”,
standard error between 1 : 20000 to 50000
 Tertiary Triangulation(3rd Order)
-Sides ranging from 1 – 15 km, angle read to 10”,
distance probable error between 1 : 10000 to 20000

Actually triangulation is best suited only to open hilly

country.

Engineering Survey – ECG422

 Shape of the triangle

1.Braced quadrilateral
5.Chain of simple triangle
3.Centerpoint pentagon

2.Centerpoint
triangle
6.Chain of braced quadrilateral
4.Quadrilateral
containing a
centerpoint

Engineering Survey – ECG422

 General procedure in triangulation
survey

 Reconnaissance of the area, to ensure the best possible

positions for stations.
 Construction of station and monuments.
 Consideration of the type of target and instrument to be
used and also the method of observation. All of these
depend on the precision required and the length of sights
involved.
 Observation of angles and baseline measurements.
 Computation baseline reduction, station and figural
adjustments of stations by direct methods. No angle less
than 30 degree

Engineering Survey – ECG422

General procedure in triangulation
survey--Cont
E” is a spherical access caused by the
curvature of the earth.

 E" = Area of triangle in km² x 5.09"

1000
or

 E" = Area of triangle x 206265

R²
 Where R = radius of the earth 6370 km.

Engineering Survey – ECG422

 Choice of Station

 i. Every station should be visible from the adjacent station.

 ii. Shape of the triangle is well condition, no angle less than

25º.

 iii. Longer sides better compared to the short one, for

accurate bisection.

 iv. The scheme should be kept as simple as possible and

future planning must be considered.

Engineering Survey – ECG422

 Seven Angle Condition

 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 360º
 1 + 2 + 3 + 4 = 180º
 3 + 4 + 5 + 6 = 180º
 5 + 6 + 7 + 8 = 180º
 7 + 8 + 1 + 2 = 180º
 1+2=5+6
 3+4=7+8

Engineering Survey – ECG422

 Adjustment Method

 a. Adjust summation of angles 1+2 + 3 + 4 + 5 + 6

+7+8 =360.

 b. Adjust (1 + 2) = (5 + 6)

 c. Adjust (3 + 4) = (7 + 8)

d. By side condition, ∑ log sin of odd angles = ∑ log

sin of even angles

Engineering Survey – ECG422