Department of Geomatics

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451 - 102 Surveying for Builders
(B.P.D.) Lecture 5 Horizontal Control Surveys
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Methods of establishing horizontal control

• Intersection
• Resection
• Traversing

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Intersection
The process of locating and co-ordinating a point
from at least two existing control stations by
observing horizontal directions at the control
points

• Calculate the bearing and distance from the known
  coordinates
• Using the sine rule deduce the other lengths of
  the triangle formed by the two known control and
  unknown point
• Establish the bearings to the unknown points from
  the known points
• Calculate the coordinates of the unknown points
  using the bearings and distances computed.

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N
C
b
a
B
A
Hint Always draw a diagram
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Intersection example
A new control point P is to be established from
existing coordinated points A and B. The
horizontal clockwise angles at A and B have been
observed as PBA 44o 52' 36" and BAP 284o 26'
38" respectively. Calculate the coordinates of
the Station P given that the coordinates of A are
3931.82mE, 7491.98m N and of B are 2959.39m E,
7487.09m N.
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Step 1 Draw Diagram
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Step 2 Compute bearing and distance between A
and B using known coordinates
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Step 3 Compute angles in the triangle formed
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Step 4 Using the sine rule compute distances in
the triangle.
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Step 4 Compute bearing of lines to unknown
point.
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Step 5 Compute coordinates of unknown point.
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Step 5 Check coordinates computed using other
known point
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Resection
Determining the position of a point by observing
horizontal directions from it to at least three
points of known position.

• Depending upon the disposition of control points,
  the unknown point can lie either inside or
  outside the triangle formed by the control
  points.
• Calculate the coordinates of the unknown point
  using Tienstra's formula.

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A
g
B
b
a
P
C
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Resection example
Angles have been observed at station P between
the coordinated control points A, B and C so that
the position of the station can be determined by
resection. Calculate the co-ordinates of P,
given Coordinates A 2876.24mE 8754.11mN
B 3810.80 7997.25 C
2959.39 7487.09
a 82.47056 b 140.9808 g 136.54864
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Step 1 Draw Diagram
A
A
g
b
B
B
a
P
C
C
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Step 2a Compute bearing between A and C using
known coordinates
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Step 2b Compute bearing between A and B using
known coordinates
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Step 2c Compute bearing between B and C using
known coordinates
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Step 3 Compute angles in the triangle formed
A
g
b
B
B
a
P
C
C
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Step 4 Compute coordinates of unknown point.
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Traversing
Rectangular co-ordinates determined from a
combination of of angle and distance measurements
along lines joining adjacent stations
X
2
Y
1
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Closed link traverse
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Closed loop traverse
X
2
1
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Traversing Fieldwork - Reconnaissance

• Locate suitable stations for traverse stations
• number of stations kept to a minimum
• lengths of line as long as possible
• stations should be intervisible,
• stations should be on firm, level ground
• traverse line of sights should be well above the
  ground
• station diagrams

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Station Marking

• Station markers must be
• permanent
• not easily disturbed
• should be clearly visible
• wooden pegs, nails, pipes, concrete
• reference or witnessing sketch

building
N
Fence post
3.4m
3.8m
3.6m
Iron bar set in concrete
Manhole cover
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Traversing Fieldwork Angular Measurement

• Forced centring - three tripod traversing
• centring errors are more significant on short
  lines

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Errors in Angular Measurement

• Inaccurate centring of theodolite or target
• non verticality of target
• inaccurate bisection of target
• parallax not eliminated
• refraction, wind and atmospheric effects
• theodolite not level and not in adjustment
• incorrect use of the theodolite
• mistakes in reading and booking

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Traversing Fieldwork Distance Measurement

• Measured using EDM or steel taping
• distance and angle measurements made
  simultaneously with total station

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Angular Misclosure
Sum of internal angles (2n -4) x 90o Sum of
external angles (2n 4) x 90o
For a link traverse Sum of angles (final
forward bearing - initial back bearing)
m x 180o
An allowable misclosure is divided equally
between the observed angles
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Bearing Calculation
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Computation of Co-ordinate Difference
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Misclosures
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Calculation of the Final Co-ordinates