Introduction to Surveying BASICS OF TRAVERSING

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Introduction to SurveyingBASICS OF TRAVERSING

• Dr Philip Collier
• Department of Geomatics
• The University of Melbourne
• p.collier_at_unimelb.edu.au
• Room D316

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Overview

• In this lecture we will cover
• Rectangular and polar coordinates
• Definition of a traverse
• Applications of traversing
• Equipment and field procedures
• Reduction and adjustment of data

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Rectangular coordinates
4
Polar coordinates
d
? whole-circle bearing d distance
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Whole circle bearings
North 0o
Bearing are measured clockwise from NORTH and
must lie in the range 0o ? ? ? 360o
4th quadrant
1st quadrant
East 90o
West 270o
3rd quadrant
2nd quadrant
South 180o
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Coordinate conversions
Polar to rectangular
Rectangular to polar
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What is a traverse?

• A polygon of 2D (or 3D) vectors
• Sides are expressed as either polar coordinates
  (?,d) or as rectangular coordinate differences
  (?E,?N)
• A traverse must either close on itself
• Or be measured between points with known
  rectangular coordinates

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Applications of traversing

• Establishing coordinates for new points

(E,N)new
(E,N)new
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Applications of traversing

• These new points can then be used as a framework
  for mapping existing features

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Applications of traversing

• They can also be used as a basis for setting out
  new work

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Equipment

• Traversing requires
• An instrument to measure angles (theodolite) or
  bearings (magnetic compass)
• An instrument to measure distances (EDM or tape)

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Measurement sequence
C
232o
168o
60.63
99.92
56o
B
352o
205o
D
232o
77.19
129.76
21o
A
32.20
118o
303o
48o
E
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Computation sequence

• Calculate angular misclose
• Adjust angular misclose
• Calculate adjusted bearings
• Reduce distances for slope etc
• Compute (?E, ?N) for each traverse line
• Calculate linear misclose
• Calculate accuracy
• Adjust linear misclose

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Calculate internal angles

• At each point
• Measure foresight bearing
• Meaure backsight bearing
• Calculate internal angle (back-fore)
• For example, at B
• Bearing to C 56o
• Bearing to A 205o
• Angle at B 205o - 56o 149o

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Calculate angular misclose
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Calculate adjusted angles
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Compute adjusted bearings

• Adopt a starting bearing
• Then, working clockwise around the traverse
• Calculate reverse bearing to backsight (forward
  bearing ?180o)
• Subtract (clockwise) internal adjusted angle
• Gives bearing of foresight
• For example (bearing of line BC)
• Adopt bearing of AB 23o
• Reverse bearing BA (23o180o) 203o
• Internal adjusted angle at B 150o
• Forward bearing BC (203o-150o) 53o

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Compute adjusted bearings
C
53o
B
150o
D
203o
A
E
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Compute adjusted bearings
C
233o
65o
168o
B
D
23o
A
E
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Compute adjusted bearings
C
53o
348o
B
121o
D
23o
227o
A
E
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Compute adjusted bearings
C
53o
168o
B
D
23o
47o
A
106o
301o
E
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Compute adjusted bearings
C
53o
168o
B
D
23o
227o
98o
A
121o
E
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(?E,?N) for each line

• The rectangular components for each line are
  computed from the polar coordinates (?,d)
• Note that these formulae apply regardless of the
  quadrant so long as whole circle bearings are used

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Vector components
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Linear misclose accuracy

• Convert the rectangular misclose components to
  polar coordinates
• Accuracy is given by

Beware of quadrant when calculating ? using tan-1
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Quadrants and tan function
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For the example

• Misclose (?E, ?N)
• (0.07, -0.05)
• Convert to polar (?,d)
• ? -54.46o (2nd quadrant) 125.53o
• d 0.09 m
• Accuracy
• 1(399.70 / 0.09) 14441

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Bowditch adjustment

• The adjustment to the easting component of any
  traverse side is given by
• ?Eadj ?Emisc side length/total perimeter
• The adjustment to the northing component of any
  traverse side is given by
• ?Nadj ?Nmisc side length/total perimeter

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The example

• East misclose 0.07 m
• North misclose 0.05 m
• Side AB 77.19 m
• Side BC 99.92 m
• Side CD 60.63 m
• Side DE 129.76 m
• Side EA 32.20 m
• Total perimeter 399.70 m

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Vector components (pre-adjustment)
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The adjustment components
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Adjusted vector components
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Introduction to SurveyingBASICS OF TRAVERSING

• Dr Philip Collier
• Department of Geomatics
• The University of Melbourne
• p.collier_at_unimelb.edu.au
• Room D316